{"id":38865,"date":"2022-04-06T15:30:26","date_gmt":"2022-04-06T10:00:26","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=38865"},"modified":"2022-04-07T11:30:14","modified_gmt":"2022-04-07T06:00:14","slug":"big-ideas-math-algebra-2-answers-chapter-7","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-7\/","title":{"rendered":"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions"},"content":{"rendered":"<p>Here, on this page, we have shared the ultimate preparation guide for high school students on algebra 2 math concepts. The given material is<strong> Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions<\/strong>. You can access and download BIM Algebra 2 Ch 7 Answer key for free of cost. So, it helps you to practice efficiently and gain more subject knowledge. Get the exercise wise chapter 7 rational functions <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers\/\">Big Ideas Math Algebra 2 Answers<\/a> from the below pdf links and start your preparation by solving the questions from various given sources covered in the BIM Algebra 2 Chapter 7 Solution Key.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 2 Answer Key Chapter 7 Rational Functions<\/h2>\n<p>In the Big Ideas Math textbook solutions algebra 2 ch 7, you can find basic &amp; strong fundamentals of Rational functons like inverse variation, graphing rational functions, adding, subtracting, mutliplying, and dividing rational expressions, and solving rational equations. By referring, practicing, and solving all the questions presented in the <em><strong>BigIdeas Math Book Algegra 2 Chapter 7 Answer Key<\/strong><\/em>, you can quickly learn the concepts and score highest rank in the exams. For students who are passionate about math skills should solve the problems in Topic-wise BIM Algebra 2 Rational functions solution key.<\/p>\n<ul>\n<li><a href=\"#Rational_Functions_Maintaining_Mathematical_Proficiency\">Rational Functions Maintaining Mathematical Proficiency &#8211; Page 357<\/a><\/li>\n<li><a href=\"#Rational_Functions_Mathematical_Practices\">Rational Functions Mathematical Practices &#8211; Page 358<\/a><\/li>\n<li><a href=\"#Lesson_7.1_Inverse_Variation\">Lesson 7.1 Inverse Variation &#8211; Page(359-364)<\/a><\/li>\n<li><a href=\"#Inverse_Variation_7.1_Exercises\">Inverse Variation 7.1 Exercises &#8211; Page(363-364)<\/a><\/li>\n<li><a href=\"#Lesson_7.2_Graphing_Rational_Functions\">Lesson 7.2 Graphing Rational Functions &#8211; Page(365-372)<\/a><\/li>\n<li><a href=\"#Graphing_Rational_Functions_7.2_Exercises\">Graphing Rational Functions 7.2 Exercises &#8211; Page(370-372)<\/a><\/li>\n<li><a href=\"#Rational_Functions_Study_Skills:_Analyzing_Your_Errors\">Rational Functions Study Skills: Analyzing Your Errors &#8211; Page 373<\/a><\/li>\n<li><a href=\"#Rational_Functions_7.1\u20137.2_Quiz\">Rational Functions 7.1\u20137.2 Quiz &#8211; Page 374<\/a><\/li>\n<li><a href=\"#Lesson_7.3_Multiplying_and_Dividing_Rational_Expressions\">Lesson 7.3 Multiplying and Dividing Rational Expressions &#8211; Page(375-382)<\/a><\/li>\n<li><a href=\"#Multiplying_and_Dividing_Rational_Expressions_7.3_Exercises\">Multiplying and Dividing Rational Expressions 7.3 Exercises &#8211; Page(380-382)<\/a><\/li>\n<li><a href=\"#Lesson_7.4_Adding_and_Subtracting_Rational_Expressions\">Lesson 7.4 Adding and Subtracting Rational Expressions &#8211; Page(383-390)<\/a><\/li>\n<li><a href=\"#Adding_and_Subtracting_Rational_Expressions_7.4_Exercises\">Adding and Subtracting Rational Expressions 7.4 Exercises &#8211; Page(388-390)<\/a><\/li>\n<li><a href=\"#Lesson_7.5_Solving_Rational_Equations\">Lesson 7.5 Solving Rational Equations &#8211; Page(391-398)<\/a><\/li>\n<li><a href=\"#Solving_Rational_Equations_7.5_Exercises\">Solving Rational Equations 7.5 Exercises &#8211; Page(396-398)<\/a><\/li>\n<li><a href=\"#Rational_Functions_Performance_Task:_Circuit_Design\">Rational Functions Performance Task: Circuit Design &#8211; Page 399<\/a><\/li>\n<li><a href=\"#Rational_Functions_Chapter_Review\">Rational Functions Chapter Review &#8211; Page(400-402)<\/a><\/li>\n<li><a href=\"#Rational_Functions_Chapter_Test\">Rational Functions Chapter Test &#8211; Page 403<\/a><\/li>\n<li><a href=\"#Rational_Functions_Cumulative_Assessment\">Rational Functions Cumulative Assessment &#8211; Page(404-405)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Rational_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Rational Functions Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Evaluate.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{3}{5}+\\frac{2}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\frac{4}{7}+\\frac{1}{6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{7}{9}-\\frac{4}{9}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{5}{12}-\\left(-\\frac{1}{2}\\right)\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{2}{7}+\\frac{1}{7}-\\frac{6}{7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{10}-\\frac{3}{4}+\\frac{2}{5}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Simplify.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\frac{\\frac{3}{8}}{\\frac{5}{6}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{\\frac{1}{4}}{-\\frac{5}{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{\\frac{2}{3}}{\\frac{2}{3}+\\frac{1}{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nFor what value of x is the expression \\(\\frac{1}{x}\\) undefined? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Rational_Functions_Mathematical_Practices\"><\/a>Rational Functions Mathematical Practices<\/h3>\n<p>Mathematically proficient students are careful about specifying units of measure and clarifying the relationship between quantities in a problem.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nYou drive a car at a speed of 60 miles per hour. What is the speed in meters per second?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nA hose carries a pressure of 200 pounds per square inch. What is the pressure in kilograms per square centimeter?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nA concrete truck pours concrete at the rate of 1 cubic yard per minute. What is the rate in cubic feet per hour?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWater in a pipe flows at a rate of 10 gallons per minute. What is the rate in liters per second?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_7.1_Inverse_Variation\"><\/a>Lesson 7.1 Inverse Variation<\/h3>\n<p><strong>Essential Question<\/strong> How can you recognize when two quantities vary directly or inversely?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Recognizing Direct VariationWork with a partner. You hang different weights from the same spring.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 1\" width=\"739\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-1.png 739w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-1-300x144.png 300w\" sizes=\"(max-width: 739px) 100vw, 739px\" \/><br \/>\na. Describe the relationship between the weight x and the distance d the spring stretches from equilibrium. Explain why the distance is said to vary directly with the weight.<br \/>\nb. Estimate the values of d from the figure. Then draw a scatter plot of the data. What are the characteristics of the graph?<br \/>\nc. Write an equation that represents d as a function of x.<br \/>\nd. In physics, the relationship between d and x is described by Hooke\u2019s Law. How would you describe Hooke\u2019s Law?<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Recognizing Inverse Variation<br \/>\nWork with a partner. The table shows the length x (in inches) and the width y (in inches) of a rectangle. The area of each rectangle is 64 square inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-2.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 2\" width=\"342\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-2.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-2-300x174.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\na. Copy and complete the table.<br \/>\nb. Describe the relationship between x and y. Explain why y is said to vary inversely with x.<br \/>\nc. Draw a scatter plot of the data. What are the characteristics of the graph?<br \/>\nd. Write an equation that represents y as a function of x.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you recognize when two quantities vary directly or inversely?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nDoes the mapping rate of the wings of a bird vary directly or inversely with the length of its wings? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether x and y show direct variation, inverse variation, or neither.<\/strong><br \/>\nQuestion 1.<br \/>\n6x = y<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nxy = \u22120.25<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny + x = 10<br \/>\nAnswer:<\/p>\n<p><strong>Tell whether x and y show direct variation, inverse variation, or neither.<\/strong><br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 3\" width=\"207\" height=\"73\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 4\" width=\"193\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p>The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2.<br \/>\nQuestion 6.<br \/>\nx = 4, y = 5<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx = 6, y = \u22121<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nx = \\(\\frac{1}{2}\\), y = 16<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 4, it takes a group of 10 volunteers 12 hours to build the playground. How long would it take a group of 15 volunteers?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Inverse_Variation_7.1_Exercises\"><\/a>Inverse Variation 7.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nExplain how direct variation equations and inverse variation equations are different.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 1\" width=\"571\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-1.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-1-300x45.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 5\" width=\"616\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-5.png 616w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-5-300x62.png 300w\" sizes=\"(max-width: 616px) 100vw, 616px\" \/><br \/>\nAnswer:<\/p>\n<p>(1): From \u00a0definition of inverse variation we have that y=a\/x where in our case a=4.This implies that inverse variation equation is<\/p>\n<p>Y=4\/x.<\/p>\n<p>(2):\u00a0 Let now ration be constant a= 4. Then we get<\/p>\n<p>y\/x=4\u00a0\u00a0\u00a0 =&gt; y =4x.<\/p>\n<p>This implies that x and y show direct variation.<\/p>\n<p>(3): From equation y=a\/x and a=4 we have that<\/p>\n<p>Y= 4\/x<\/p>\n<p>It implies that x and y show inverse variation.<\/p>\n<p>(4): By equation x y =4 it implies that y=4\/x<\/p>\n<p>This equation means that x and y show inverse variation.<\/p>\n<p>The different question is (2): where x and y show \u00a0\u00a0direct variation<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, tell whether x and y show direct variation, inverse variation, or neither.<\/strong><br \/>\nQuestion 3.<br \/>\ny = \\(\\frac{2}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 3\" width=\"553\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-3.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-3-300x47.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 4.<br \/>\nxy = 12<br \/>\nAnswer:<\/p>\n<p>Given equation\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Solved for y\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Type of variation<\/p>\n<p>xy=12\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Y=12\/x\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0inverse variation<\/p>\n<p>&nbsp;<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{y}{x}\\) = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 5\" width=\"538\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-5.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-5-300x47.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 6.<br \/>\n4x = y<br \/>\nAnswer:<\/p>\n<p>By definition ,x and y show direct variation<\/p>\n<p>Question 7.<br \/>\ny = x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 7\" width=\"554\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-7.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-7-300x33.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 8.<br \/>\nx + y = 6<br \/>\nAnswer:<\/p>\n<p>Given Equation\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Solved for\u00a0 y\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Types of variation<\/p>\n<p>x+y=6\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Add -x to both sides\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 X and y shows no variation<\/p>\n<p>Y= -x+6<\/p>\n<p><span style=\"font-size: 16px;\">Question 9.<\/span><\/p>\n<p>8y = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 9\" width=\"542\" height=\"81\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-9.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-9-300x45.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p>Question 10.<br \/>\nxy = \\(\\frac{1}{5}\\)<br \/>\nAnswer:<\/p>\n<p>Solve for y . Divide equation with x<\/p>\n<p>Xy = 1\/5<br \/>\nY=1\/5x=( 1\/5)\/x<\/p>\n<p>inverse variation<\/p>\n<p>&nbsp;<\/p>\n<p><strong>In Exercises 11\u201314, tell whether x and y show direct variation, inverse variation, or neither.<\/strong><br \/>\nQuestion 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 6\" width=\"227\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p>y\/x\u00a0 \u00a0 132\/12=11\u00a0\u00a0\u00a0 198\/18 =11\u00a0\u00a0 235\/23 =11\u00a0\u00a0 319\/29\u00a0 =11\u00a0\u00a0\u00a0 374\/34=11<\/p>\n<p>The products are not constant , and the rations are constant .<\/p>\n<p>X and y show direct variation .<\/p>\n<p>&nbsp;<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-7.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 7\" width=\"232\" height=\"75\" \/><br \/>\nAnswer:<\/p>\n<table width=\"1067\">\n<tbody>\n<tr>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><b>xy<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0 20.25<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0 56.25 <\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0 144\u00a0\u00a0\u00a0 <\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 506.25<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 900<\/b><\/td>\n<\/tr>\n<tr>\n<td width=\"178\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 y\/ x<\/td>\n<td width=\"178\">\u00a0\u00a0\u00a0\u00a0\u00a0 13.5\/1.5=9<\/td>\n<td width=\"178\">22.5\/2.5=9<\/td>\n<td width=\"178\">36\/4=9<\/td>\n<td width=\"178\">67.5\/7.5=9<\/td>\n<td width=\"178\">90\/10=9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The products are not constant , and the rations are constant .<\/p>\n<p>X and y show direct variation .<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-8.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 8\" width=\"229\" height=\"71\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 13\" width=\"615\" height=\"198\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-13.png 615w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-13-300x97.png 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-9.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 9\" width=\"229\" height=\"77\" \/><br \/>\nAnswer:<\/p>\n<table width=\"1067\">\n<tbody>\n<tr>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><b>xy<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 64<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 55<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 62<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 63<\/b><\/td>\n<td width=\"178\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 66<\/b><\/td>\n<\/tr>\n<tr>\n<td width=\"178\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 y\/ x<\/td>\n<td width=\"178\">\u00a0\u00a0\u00a0\u00a0\u00a0 16\/4=4<\/td>\n<td width=\"178\">\u00a0 11\/5=2.2<\/td>\n<td width=\"178\">10\/6.2=1.612<\/td>\n<td width=\"178\">9\/7=1.285<\/td>\n<td width=\"178\">6\/11=0.545<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The products are not constant, and the ratios are not constant.<\/p>\n<p>X and y show no variation .<\/p>\n<p>&nbsp;<\/p>\n<p>In Exercises 15\u201322, the variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 3.<br \/>\nQuestion 15.<br \/>\nx = 5, y =\u22124<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 15\" width=\"529\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-15.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-15-300x129.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/p>\n<p>Question 16.<br \/>\nx = 1, y = 9<br \/>\nAnswer:<\/p>\n<p>Y=a\/x<\/p>\n<p>Plug \u00a0x=1, y=9 into equation to determine a.<\/p>\n<p>9=a\/1<\/p>\n<p>a =9.1=9<\/p>\n<p>The inverse variation equation is y= 9\/x<\/p>\n<p>When x=3,<\/p>\n<p>Y=9\/3=3<\/p>\n<p>Question 17.<br \/>\nx =\u22123, y = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 17\" width=\"546\" height=\"231\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-17.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-17-300x127.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 18.<br \/>\nx = 7, y = 2<br \/>\nAnswer:<\/p>\n<p>Y=a\/x<\/p>\n<p>Plug \u00a0x=7, y=2 into equation to determine a.<\/p>\n<p>7=a\/2<\/p>\n<p>a=7. 2=14<\/p>\n<p>The inverse variation equation is y=14\/x<\/p>\n<p>When x=3<\/p>\n<p>Y=14\/3<\/p>\n<p>Question 19.<br \/>\nx = \\(\\frac{3}{4}\\), y = 28<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 19\" width=\"508\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-19.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-19-300x167.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Question 20.<br \/>\nx = \u22124, y = &#8211;\\(\\frac{5}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Y=a\/x<\/p>\n<p>Plug \u00a0x= -4\u00a0 , \u00a0y=-5\/4 into equation to determine a.<\/p>\n<p>-5\/4\u00a0 = a\/-4<\/p>\n<p>a =-5\/4\u00a0 . (-4)=5<\/p>\n<p>The inverse variation equation is y=5\/x<\/p>\n<p>When x=3<\/p>\n<p>Y=5\/3<\/p>\n<p>Question 21.<br \/>\nx = \u221212, y = \u2212\\(\\frac{6}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 21\" width=\"567\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-21.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-21-300x98.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 22.<br \/>\nx = \\(\\frac{5}{3}\\), y = \u22127<br \/>\nAnswer:<\/p>\n<p>Y=a\/x<\/p>\n<p>Plug \u00a0x= 5\/3\u00a0 , \u00a0y=-7 into equation to determine a.<\/p>\n<p>-7 =a\/5\/3<\/p>\n<p>A=-7 . 5\/3 = &#8211; 35\/3<\/p>\n<p>The inverse variation equation is y=-35\/3\/x<\/p>\n<p>When x=3<\/p>\n<p>Y=-35\/3\/3=-35\/9<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 23 and 24, the variables x and y vary inversely. Describe and correct the error in writing an equation relating x and y.<br \/>\nQuestion 23.<br \/>\nx = 8, y = 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-10.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 10\" width=\"177\" height=\"141\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 23\" width=\"539\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-23.png 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-23-300x149.png 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 24.<br \/>\nx = 5, y = 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-11.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 11\" width=\"185\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p>Every thing is correct except last row when they plug a = 10 into starting equation . it shoulds be like this<\/p>\n<p>a=10<\/p>\n<p>Xy=a<\/p>\n<p>Xy=10, divide with x<\/p>\n<p>Y=10\/x<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe number y of songs that can be stored on an MP3 player varies inversely with the average size x of a song. A certain MP3 player can store 2500 songs when the average size of a song is 4 megabytes (MB).<br \/>\na. Make a table showing the numbers of songs that will fit on the MP3 player when the average size of a song is 2 MB, 2.5 MB, 3 MB, and 5 MB.<br \/>\nb. What happens to the number of songs as the average song size increases?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-25.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 25\" width=\"564\" height=\"658\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-25.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-25-257x300.png 257w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nWhen you stand on snow, the average pressure P (in pounds per square inch) that you exert on the snow varies inversely with the total area A (in square inches) of the soles of your footwear. Suppose the pressure is 0.43 pound per square inch when you wear the snowshoes shown. Write an equation that gives P as a function of A. Then find the pressure when you wear the boots shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-12.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 12\" width=\"258\" height=\"201\" \/><br \/>\nAnswer:<\/p>\n<p>The general equation for inverse variation is<\/p>\n<p>Y=a\/x<\/p>\n<p>Let y=P where P is average pressure \u00a0\u00a0on snow and x =A is the total area .<\/p>\n<p>If we wear the snowshoes then the \u00a0\u00a0P is 0.43 and A=360. Using the equation about we have that<\/p>\n<p>P=a\/A<\/p>\n<p>0.43=a\/360<\/p>\n<p>A=0.43.360=154.8<\/p>\n<p>It implies that \u00a0\u00a0P=154.8\/A<\/p>\n<p>Now \u00a0, if you boots then A=60. Using the equation about we have that<\/p>\n<p>P=a\/A<\/p>\n<p>0.43=a\/60<\/p>\n<p>A=0.43.60=25.8<\/p>\n<p>It implies that<\/p>\n<p>P=25.8\/A<\/p>\n<p>&nbsp;<\/p>\n<p>Question 27.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nComputer chips are etched onto silicon wafers. The table compares the area A (in square millimeters) of a computer chip with the number c of chips that can be obtained from a siliconwafer. Write a model that gives c as a function of A. Then predict the number of chips per wafer when the area of a chip is 81 square millimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 13\" width=\"316\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-13.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-13-300x69.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-27.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 27\" width=\"583\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-27.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-27-300x173.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDoes the graph of f represent inverse variation or direct variation? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-14.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 14\" width=\"117\" height=\"190\" \/><br \/>\nAnswer:<\/p>\n<p>As x increases, y increases as well, so product x. y cannot possibly be constant.<\/p>\n<p>This means that x and y show direct variation .<\/p>\n<p>Question 29.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou have enough money to buy 5 hats for $10 each or 10 hats for $5 each. Your friend says this situation represents inverse variation. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-29.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 29\" width=\"566\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-29.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-29-300x33.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe weight w (in pounds) of an object varies inversely with the square of the distance d (in miles) of the object from the center of Earth. At sea level (3978 miles from the center of theEarth), an astronaut weighs 210 pounds. How much does the astronaut weigh 200 miles above sea level?<br \/>\nAnswer:<\/p>\n<p>Write the equation that represents\u00a0 given variation :<\/p>\n<p>W=a\/d<sup>2<\/sup> &#8211; there is d<sup>2<\/sup> in denominator because w varies inversely \u00a0\u00a0with square of the distance \u00a0.<\/p>\n<p>Plug d=3978 and w=210 into equation to determine a.<\/p>\n<p>210 = a\/3978<sup>2<\/sup><\/p>\n<p>A=210. 3978<sup>2<\/sup> = 3,323,141,640<\/p>\n<p>Equation :<\/p>\n<p>W = 3,323,141,640\/d<sup>2<\/sup><\/p>\n<p>When d = 3978+200 = 4178:<\/p>\n<p>W = 3,323,141,640\/4178<sup>2<\/sup> = 190<\/p>\n<p>Question 31.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe a real-life situation that can be modeled by an inverse variation equation.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-31.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 31\" width=\"520\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-31.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-31-300x35.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSuppose x varies inversely with y and y varies inversely with z. How does x vary with z? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Y=b\/z<\/p>\n<p>From first equation:<\/p>\n<p>X=a\/y, multiply with y<\/p>\n<p>X y= a, divide\u00a0 with x<\/p>\n<p>Y=a\/x<\/p>\n<p>Substitute this y with y in equation with z:<\/p>\n<p>Y=b\/z<\/p>\n<p>a\/x = b\/z, multiply with x z<\/p>\n<p>a z=b z<\/p>\n<p>x=a\/b z<\/p>\n<p>x varies directly with z.<\/p>\n<p>Question 33.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nTo balance the board in the diagram, the distance (in feet) of each animal from the center of the board must vary inversely with its weight (in pounds). What is the distance of each animal from the fulcrum? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-15.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 15\" width=\"311\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-15.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-15-300x99.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 33\" width=\"525\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-33.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-33-300x158.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency Divide.<\/strong><br \/>\nQuestion 34.<br \/>\n(x<sup>2<\/sup> + 2x \u2212 99) \u00f7 (x + 11)<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_204306-1.jpg\" alt=\"\" width=\"310\" height=\"240\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_204306-1.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_204306-1-300x232.jpg 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 35.<br \/>\n(3x<sup>4<\/sup> \u2212 13x<sup>2<\/sup> \u2212 x<sup>3<\/sup> + 6x \u2212 30) \u00f7 (3x<sup>2<\/sup> \u2212 x + 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 35\" width=\"568\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-35.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-35-300x128.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p><strong>Graph the function. Then state the domain and range.<\/strong><br \/>\nQuestion 36.<br \/>\nf(x) = 5<sup>x<\/sup> + 4<br \/>\nAnswer:<\/p>\n<p>First graph g(x)= 5<sup>x<\/sup>. Then translate it 4 units up\u00a0 to obtain f(x).<\/p>\n<p>On graph :<\/p>\n<p>Red \u2013 g(x)<\/p>\n<p>Blue \u2013 f(x)<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_204223-1.jpg\" alt=\"\" width=\"329\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_204223-1.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_204223-1-300x192.jpg 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Domain of f is all real number and range of f is (4, \u221e)<\/p>\n<p>Question 37.<br \/>\ng(x) = e<sup>x-1<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 37\" width=\"526\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-37.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-37-300x160.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 38.<br \/>\ny = ln 3x &#8211; 6<br \/>\nAnswer:<\/p>\n<p>First graph g(x)=In 3x. Then translate it six units down\u00a0 to obtain f(x).<\/p>\n<p>On graph :<\/p>\n<p>Red \u2013 g(x)<\/p>\n<p>Blue \u2013 f(x)<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_220121.jpg\" alt=\"\" width=\"327\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_220121.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_220121-300x191.jpg 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Domain of f is all positive number real numbers,(0, \u221e) and range of f is (-\u221e, \u221e)- all real numbers.<\/p>\n<p>Question 39.<br \/>\nln(x) = 2 ln (x + 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions 7.1 a 39\" width=\"578\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-39.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-7.1-a-39-300x147.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<h3><a id=\"Lesson_7.2_Graphing_Rational_Functions\"><\/a>Lesson 7.2 Graphing Rational Functions<\/h3>\n<p><strong>Essential Question<\/strong> What are some of the characteristics of the graph of a rational function?<br \/>\nThe parent function for rational functions with a linear numerator and a linear denominator is<br \/>\nf(x) = \\(\\frac{1}{x}\\). Parent function<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 1\" width=\"205\" height=\"153\" \/><br \/>\nThe graph of this function, shown at the right, is a hyperbola.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Identifying Graphs of Rational Functions<br \/>\nWork with a partner. Each function is a transformation of the graph of the parent function f(x) = \\(\\frac{1}{x}\\). Match the function with its graph. Explain your reasoning. Then describe the transformation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 2\" width=\"490\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-2.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-2-277x300.png 277w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nWhat are some of the characteristics of the graph of a rational function?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nDetermine the intercepts, asymptotes, domain, and range of the rational function g(x) = \\(\\frac{x-a}{x-b}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 3\" width=\"231\" height=\"152\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Question 1.<br \/>\nGraph g(x) = \\(\\frac{-6}{x}\\). Compare the graph with the graph of f(x) = \\(\\frac{1}{x}\\).<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. State the domain and range.<\/strong><br \/>\nQuestion 2.<br \/>\ny = \\(\\frac{3}{x}\\) &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = \\(\\frac{-1}{x + 4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ny = \\(\\frac{1}{x &#8211; 1}\\) + 5<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. State the domain and range.<\/strong><br \/>\nQuestion 5.<br \/>\nf(x) = \\(\\frac{x-1}{x+3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nf(x) = \\(\\frac{2x+1}{4x-2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nf(x) = \\(\\frac{-3x+2}{-x-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nRewrite g(x) = \\(\\frac{2x+3}{x+1}\\) in the form g(x) = \\(\\frac{a}{x-h}\\). Graph the function.<br \/>\nDescribe the graph of g as a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nHow do the answers in Example 5 change when the cost of the 3-D printer is $800?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Rational_Functions_7.2_Exercises\"><\/a>Graphing Rational Functions 7.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe function y = \\(\\frac{7}{x+2}\\) has a(n) __________ of all real numbers except 3 and a(n) __________ of all real numbers except \u22124.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 1\" width=\"579\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-1-300x47.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nIs f(x) = \\(\\frac{-3 x+5}{2^{x}+1}\\) a rational function? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Consider function f given by<\/p>\n<p>f(x) =-3x+5\/2<sup>x<\/sup> +1<\/p>\n<p>We know that the rational function has form<\/p>\n<p>Y=a x +b\/ c x +d<\/p>\n<p>Where a, b,c, d are constant such that c x+d \u2260 0<\/p>\n<p>Since 2<sup>x<\/sup> is exponential function then the given function is not rational<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, graph the function. Compare the graph with the graph of f(x) = \\(\\frac{1}{x}\\).<\/strong><br \/>\nQuestion 3.<br \/>\ng(x) = \\(\\frac{3}{x}\\)<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-46063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 3\" width=\"583\" height=\"743\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-3.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-3-235x300.png 235w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 4.<br \/>\ng(x) = \\(\\frac{10}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Step:1<\/p>\n<p>The function is of form g(x)= a\/x, so the asymptotes are x=0 and y=0<\/p>\n<p>Step:2<\/p>\n<p>Make a table of value and plot the points.<\/p>\n<p>Include both positive and negative values of x.<\/p>\n<table style=\"height: 102px;\" width=\"1065\">\n<tbody>\n<tr>\n<td width=\"120\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 x<\/b><\/td>\n<td width=\"158\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -3<\/b><\/td>\n<td width=\"158\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -2<\/b><\/td>\n<td width=\"158\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1<\/b><\/td>\n<td width=\"158\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 1<\/b><\/td>\n<td width=\"158\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2<\/b><\/td>\n<td width=\"158\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/b><\/td>\n<\/tr>\n<tr>\n<td width=\"120\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 y<\/td>\n<td width=\"158\">\u00a0\u00a0\u00a0\u00a0\u00a0 -10\/3<\/td>\n<td width=\"158\">\u00a0\u00a0\u00a0\u00a0 -5<\/td>\n<td width=\"158\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -10<\/td>\n<td width=\"158\">\u00a0\u00a0\u00a0\u00a0\u00a0 10<\/td>\n<td width=\"158\">\u00a0\u00a0\u00a0\u00a0\u00a0 5<\/td>\n<td width=\"158\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 10\/3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-size: 16px;\">Step=3<\/span><\/p>\n<p><span style=\"font-size: 16px;\">On graph :<\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_222115.jpg\" alt=\"\" width=\"348\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_222115.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_222115-300x175.jpg 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Red \u2013 f(x)= 1\/x<\/p>\n<p>Blue \u2013 g(x) = 10\/x<\/p>\n<p>Question 5.<br \/>\ng(x) = \\(\\frac{-5}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 5\" width=\"585\" height=\"746\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-5.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-5-235x300.png 235w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 6.<br \/>\ng(x) = \\(\\frac{-9}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Step:1<\/p>\n<p>The function is of form g(x)= a\/x, so the asymptotes are x=0 and y=0<\/p>\n<p>Step:2<\/p>\n<p>Make a table of value and plot the points.<\/p>\n<p>Include both positive and negative values of x.<\/p>\n<table width=\"762\">\n<tbody>\n<tr>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0 x<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0 -3<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 -2<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0 -1<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0 1<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/b><\/td>\n<\/tr>\n<tr>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 y<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 9\/2<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0\u00a0 9<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 -9<\/td>\n<td width=\"109\">\u00a0\u00a0 -9\/2<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0\u00a0 -3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-size: 16px;\">Step=3<\/span><\/p>\n<p><span style=\"font-size: 16px;\">On graph :<\/span><\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_222115-1.jpg\" alt=\"\" width=\"317\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_222115-1.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_222115-1-300x175.jpg 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Red \u2013 f(x)= 1\/x<\/p>\n<p>Blue \u2013 g(x) = -9\/x<\/p>\n<p>The graph of g lies further from axes than the graph of f. Both have the same asymptotes, domain and range . Graph of g lies in second and fourth quadrants \u00a0, and graph of f lies and third quadrants<\/p>\n<p>Question 7.<br \/>\ng(x) = \\(\\frac{15}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 7\" width=\"589\" height=\"746\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-7.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-7-237x300.png 237w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 8.<br \/>\ng(x) = \\(\\frac{-12}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Step 1<\/p>\n<p>The function is of form g(x)= a\/x, so the asymptotes are x=0 and y=0<\/p>\n<p>Step 2<\/p>\n<p>Make a table of value and plot the points.<\/p>\n<p>Include both positive and negative values of x.<\/p>\n<table style=\"height: 113px;\" width=\"806\">\n<tbody>\n<tr>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0 x<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0 -3<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 -2<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0 -1<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0 1<\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 2\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/td>\n<td width=\"109\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/b><\/td>\n<\/tr>\n<tr>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 y<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0\u00a0 4<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 6<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 12<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0 -12<\/td>\n<td width=\"109\">\u00a0\u00a0 -6<\/td>\n<td width=\"109\">\u00a0\u00a0\u00a0\u00a0\u00a0 -4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Step 3<\/p>\n<p>On graph :<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_224108.jpg\" alt=\"\" width=\"269\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_224108.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_224108-300x178.jpg 300w\" sizes=\"(max-width: 269px) 100vw, 269px\" \/><\/p>\n<p>Red \u2013 f(x)= 1\/x<\/p>\n<p>Blue \u2013 g(x) = -12\/x<\/p>\n<p>The graph of g lies further from axes than the graph of f. Both have the same asymptotes, domain and range . Graph of g lies in second and fourth quadrants \u00a0, and graph of f lies and third quadrants.<\/p>\n<p>Question 9.<br \/>\ng(x) = \\(\\frac{-0.5}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 9\" width=\"611\" height=\"741\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-9.png 611w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-9-247x300.png 247w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><\/p>\n<p>Question 10.<br \/>\ng(x) = \\(\\frac{0.1}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Step 1<\/p>\n<p>The function is of form g(x)= a\/x, so the asymptotes are x=0 and y=0<\/p>\n<p>step 2<\/p>\n<p>Make a table of value and plot the points.<\/p>\n<p>Include both positive and negative values of x.<\/p>\n<table width=\"1067\">\n<tbody>\n<tr>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 x<\/b><\/td>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -3<\/b><\/td>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -2<\/b><\/td>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -1<\/b><\/td>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0 1<\/b><\/td>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 2<\/b><\/td>\n<td width=\"152\"><b>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3<\/b><\/td>\n<\/tr>\n<tr>\n<td width=\"152\">\u00a0\u00a0\u00a0\u00a0\u00a0 y<\/td>\n<td width=\"152\">\u00a0-0.033<\/td>\n<td width=\"152\">\u00a0\u00a0\u00a0\u00a0 -0.05<\/td>\n<td width=\"152\">\u00a0\u00a0\u00a0\u00a0\u00a0 -0.1<\/td>\n<td width=\"152\">\u00a0\u00a0\u00a0 0.1<\/td>\n<td width=\"152\">\u00a0\u00a0\u00a0\u00a0\u00a0 0.05<\/td>\n<td width=\"152\">\u00a0\u00a0\u00a0\u00a0\u00a0 0.033<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Step 3<\/p>\n<p>On graph :<\/p>\n<p>Red \u2013 f(x)= 1\/x<\/p>\n<p>Blue \u2013 g(x) = -0.1\/x<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_224906.jpg\" alt=\"\" width=\"309\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_224906.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_224906-300x173.jpg 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>The graph of g lies closer to axes than the graph of f . Both graphs lie in first and third quadrants and have the same asymptotes, domain and range<\/p>\n<p>&nbsp;<\/p>\n<p><strong>In Exercises 11\u201318, graph the function. State the domain and range.<\/strong><br \/>\nQuestion 11.<br \/>\ng(x) = \\(\\frac{4}{x}\\)+ 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 11\" width=\"591\" height=\"661\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-11.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-11-268x300.png 268w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 12.<br \/>\ny = \\(\\frac{2}{x}\\) \u2212 3<br \/>\nAnswer:<\/p>\n<p>Consider function f given by<\/p>\n<p>F(x)=2\/x\u00a0\u00a0 -3<\/p>\n<p>We have that\u00a0\u00a0 x=0<\/p>\n<p>Is vertical asymptote \u00a0.The horizontal asymptote is<\/p>\n<p>Y=-3<\/p>\n<p>Plot point to the left of the vertical\u00a0 \u00a0asymptote, such as (-1,-5),(-4,-7\/2),<\/p>\n<p>And (-2\/5 , -8 ).Plot points to the right of the vertical asymptote, such as (2,-2),(1\/2,1) and (4,-5\/2).<\/p>\n<p>The domain is all real number except x=0 and the range is all real numbers except y=-3<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_225705.jpg\" alt=\"\" width=\"347\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_225705.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_225705-300x211.jpg 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 13.<br \/>\nh(x) = \\(\\frac{6}{x-1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-13.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 13\" width=\"593\" height=\"684\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-13.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-13-260x300.png 260w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 14.<br \/>\ny = \\(\\frac{1}{x+2}\\)<br \/>\nAnswer:<\/p>\n<p>Consider function f given by<\/p>\n<p>f(x)=1\/x+2<\/p>\n<p>From x+2 =0 we get that\u00a0 x =-2<\/p>\n<p>is vertical asymptote \u00a0.The horizontal asymptote is<\/p>\n<p>Y=0<\/p>\n<p>Plot point to the left of the vertical\u00a0 \u00a0asymptote, such as (-3,-1),(-4,-1\/2),<\/p>\n<p>And (-7 , -1\/5).Plot points to the right of the vertical asymptote, such as (-1\/2,-2),(0,1\/2) and (3,1\/5).<\/p>\n<p>The domain is all real number except x= -2 and the range is all real numbers except y=0<\/p>\n<p>&nbsp;<\/p>\n<p><sup>\u00a0<\/sup><img loading=\"lazy\" class=\"alignnone wp-image-87832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_231111.jpg\" alt=\"\" width=\"346\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_231111.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_231111-300x186.jpg 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Question 15.<br \/>\nh(x) = \\(\\frac{-3}{x+2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-15.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 15\" width=\"587\" height=\"678\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-15.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-15-260x300.png 260w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = \\(\\frac{-2}{x-7}\\)<br \/>\nAnswer:<\/p>\n<p>Consider function f given by<\/p>\n<p>f(x)=-2\/x-7<\/p>\n<p>From x+2 =0 we get that\u00a0 x = 7<\/p>\n<p>is vertical asymptote \u00a0.The horizontal asymptote is<\/p>\n<p>Y=0<\/p>\n<p>Plot point to the left of the vertical\u00a0 \u00a0asymptote, such as (5,1),(3,1\/2),<\/p>\n<p>And (6 , 2).Plot points to the right of the vertical asymptote, such as (8,-2),(9,1) and (11,-1\/2).<\/p>\n<p>The domain is all real number except x= \u00a07and the range is all real numbers except y=0<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_232332.jpg\" alt=\"\" width=\"433\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_232332.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_232332-300x180.jpg 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Question 17.<br \/>\ng(x) = \\(\\frac{-3}{x-4}\\) \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-17.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 17\" width=\"568\" height=\"699\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-17.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-17-244x300.png 244w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 18.<br \/>\ny = \\(\\frac{10}{x+7}\\) \u2212 5<br \/>\nAnswer:<\/p>\n<p>Consider function f given by<\/p>\n<p>f(x)=10\/x+7\u00a0\u00a0 &#8211;\u00a0 5<\/p>\n<p>From x+2 =0 we get that\u00a0 x = -7<\/p>\n<p>is vertical asymptote \u00a0.The horizontal asymptote is<\/p>\n<p>Y=-5<\/p>\n<p>Plot point to the left of the vertical\u00a0 \u00a0asymptote, such as (-17,-6),(-12,-7),<\/p>\n<p>And (-8 , -15).Plot points to the right of the vertical asymptote, such as (-5,0),(-2,-3) and (3,-4).<\/p>\n<p>The domain is all real number except x= \u00a0-7and the range is all real numbers except y=-5<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_232654.jpg\" alt=\"\" width=\"408\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_232654.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_232654-300x231.jpg 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 19 and 20, describe and correct the error in graphing the rational function.<br \/>\nQuestion 19.<br \/>\ny = \\(\\frac{-8}{x}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 4\" width=\"241\" height=\"192\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-19.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 19\" width=\"563\" height=\"347\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-19.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-19-300x185.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 20.<br \/>\ny = \\(\\frac{2}{x-1}\\) &#8211; 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 5\" width=\"237\" height=\"203\" \/><br \/>\nAnswer:<\/p>\n<p>Vertical asymptote is incorrect.<\/p>\n<p>It should be x-1=0<\/p>\n<p>X=1<\/p>\n<p>Correct \u00a0\u00a0graph :<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_233634.jpg\" alt=\"\" width=\"378\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_233634.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_233634-300x173.jpg 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p><strong>ANALYZING RELATIONSHIPS<\/strong> In Exercises 21\u201324, match the function with its graph. Explain your reasoning.<br \/>\nQuestion 21.<br \/>\ng(x) = \\(\\frac{2}{x-3}\\) + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-21.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 21\" width=\"560\" height=\"32\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-21.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-21-300x17.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 22.<br \/>\nh(x) = \\(\\frac{2}{x+3}\\) + 1<br \/>\nAnswer:<\/p>\n<p>The graph is A because the asymptotes are x=-3 and y=1<\/p>\n<p>Question 23.<br \/>\nf(x) = \\(\\frac{2}{x-3}\\) \u2212 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-23.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 23\" width=\"581\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-23.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-23-300x17.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 24.<br \/>\ny = \\(\\frac{2}{x+3}\\) \u2212 1<br \/>\nAnswer:<\/p>\n<p>The graph is D\u00a0 because the asymptotes are x=-3 and\u00a0 y=1<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-38888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-6.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 6.1\" width=\"357\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-6.1.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-6.1-300x234.png 300w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><\/p>\n<p><strong>In Exercises 25\u201332, graph the function. State the domain and range.<\/strong><br \/>\nQuestion 25.<br \/>\nf(x) = \\(\\frac{x+4}{x-3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-25.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 25.1\" width=\"566\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-25.1.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-25.1-300x185.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-25.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 25.2\" width=\"565\" height=\"437\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-25.2.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-25.2-300x232.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 26.<br \/>\ny = \\(\\frac{x-1}{x+5}\\)<br \/>\nAnswer:<\/p>\n<p>Consider function f given by<\/p>\n<p>Y=x-1\/x+5<\/p>\n<p>We know that the rational function has form y= a x+ b\/cx +d<\/p>\n<p>Where a,b,c,d are constant such that cx+d 0 .<\/p>\n<p>From x+5 =0 we get that\u00a0 x = -5<\/p>\n<p>is vertical asymptote \u00a0\u00a0.The horizontal asymptote is<\/p>\n<p>Y=a\/c = 1\/1 =1<\/p>\n<p>Plot point to the left of the vertical\u00a0 \u00a0asymptote, such as (-11,2),(-8,3),<\/p>\n<p>And(-7 , -4).Plot points to the right of the vertical asymptote, such as (-4,-5),(-2,-1) and (1,0).<\/p>\n<p>The domain is all real number except x= \u00a0-5and the range is all real numbers except y=1<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-87842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_234754.jpg\" alt=\"\" width=\"425\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_234754.jpg 705w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Screenshot_2021_0408_234754-300x262.jpg 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>Question 27.<br \/>\ny = \\(\\frac{x+6}{4x-8}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-27.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 27.1\" width=\"582\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-27.1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-27.1-300x198.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-27.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 27.2\" width=\"561\" height=\"449\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-27.2.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-27.2-300x240.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 28.<br \/>\nh(x) = \\(\\frac{8x+3}{2x-6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nf(x) = \\(\\frac{-5x+2}{4x+5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-29.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 29.1\" width=\"573\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-29.1.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-29.1-300x210.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-29.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 29.2\" width=\"557\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-29.2.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-29.2-300x255.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 30.<br \/>\ng(x) = \\(\\frac{6x-1}{3x-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nh(x) = \\(\\frac{-5x}{-2x-3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-31.1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 31.1\" width=\"595\" height=\"341\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-31.1.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-31.1-300x172.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-31.2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 31.2\" width=\"553\" height=\"425\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-31.2.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-31.2-300x231.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 32.<br \/>\ny = \\(\\frac{-2x+1}{-x+10}\\)<br \/>\nAnswer:<\/p>\n<p>In Exercises 33\u201340, rewrite the function in the form g(x) = \\(\\frac{a}{x-h}\\) + k. Graph the function. Describe the graph of g as a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nQuestion 33.<br \/>\ng(x) = \\(\\frac{5x+6}{x+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-33.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 33\" width=\"573\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-33.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-33-287x300.png 287w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 34.<br \/>\ng(x) = \\(\\frac{7x+4}{x-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ng(x) = \\(\\frac{2x-4}{x-5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-35.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 35\" width=\"554\" height=\"641\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-35.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-35-259x300.png 259w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 36.<br \/>\ng(x) = \\(\\frac{4x-11}{x-2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ng(x) = \\(\\frac{x+18}{x-6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-37.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 37\" width=\"592\" height=\"610\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-37.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-37-291x300.png 291w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 38.<br \/>\ng(x) = \\(\\frac{x+2}{x-8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\ng(x) = \\(\\frac{7x-20}{x+13}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-39.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 39\" width=\"561\" height=\"601\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-39.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-39-280x300.png 280w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 40.<br \/>\ng(x) = \\(\\frac{9x-3}{x+7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYour school purchases a math software program. The program has an initial cost of $500 plus $20 for each student that uses the program.<br \/>\na. Estimate how many students must use the program for the average cost per student to fall to $30.<br \/>\nb. What happens to the average cost as more students use the program?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-41.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 41\" width=\"582\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-41.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-41-300x161.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nTo join a rock climbing gym, you must pay an initial fee of $100 and a monthly fee of $59.<br \/>\na. Estimate how many months you must purchase a membership for the average cost per month to fall to $69.<br \/>\nb. What happens to the average cost as the number of months that you are a member increases?<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWhat is the vertical asymptote of the graph of the function y = \\(\\frac{2}{x+4}\\) + 7?<br \/>\nA. x =\u22127<br \/>\nB. x = \u22124<br \/>\nC. x = 4<br \/>\nD. x = 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-43.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 43\" width=\"341\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-43.png 341w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-43-300x29.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhat are the x-intercept(s) of the graph of the function y = \\(\\frac{x-5}{x^{2}-1}\\)?<br \/>\nA. 1, \u22121<br \/>\nB. 5<br \/>\nC. 1<br \/>\nD. \u22125<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe time t (in seconds) it takes for sound to travel 1 kilometer can be modeled by<br \/>\nt = \\(\\frac{1000}{06T+331}\\)<br \/>\nwhere T is the air temperature (in degrees Celsius).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 6\" width=\"256\" height=\"163\" \/><br \/>\na. You are 1 kilometer from a lightning strike. You hear the thunder 2.9 seconds later. Use a graph to fund the approximate air temperature.<br \/>\nb. Find the average rate of change in the time it takes sound to travel 1 kilometer as the air temperature increases from 0\u00b0C to 10\u00b0C.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-45.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 45\" width=\"577\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-45.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-45-300x94.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA business is studying the cost to remove a pollutant from the ground at its site. The function y = \\(\\frac{15x}{1.1-x}\\) models the estimated cost y (in thousands of dollars) to remove x percent (expressed as a decimal) of the pollutant.<br \/>\na. Graph the function. Describe a reasonable domain and range.<br \/>\nb. How much does it cost to remove 20% of the pollutant? 40% of the pollutant? 80% of the pollutant? Does doubling the percentage of the pollutant removed double the cost? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 47\u201350, use a graphing calculator to graph the function. Then determine whether the function is even, odd, or neither.<br \/>\nQuestion 47.<br \/>\nh(x) = \\(\\frac{6}{x^{2}+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-47.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 47\" width=\"544\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-47.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-47-300x90.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = \\(\\frac{2 x^{2}}{x^{2}-9}\\)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\ny = \\(\\frac{x^{3}}{3 x^{2}+x^{4}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-49.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 49\" width=\"557\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-49.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-49-300x89.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 50.<br \/>\nf(x) = \\(\\frac{4 x^{2}}{2 x^{3}-x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims it is possible for a rational function to have two vertical asymptotes. Is your friend correct? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-51.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 51\" width=\"564\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-51.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-51-300x77.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph of f to determine the equations of the asymptotes. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-7.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 7\" width=\"227\" height=\"192\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nIn what line(s) is the graph of y = \\(\\frac{1}{x}\\) symmetric? What does this symmetry tell you about the inverse of the function f(x) = \\(\\frac{1}{x}\\)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-53.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 53\" width=\"574\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-53.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-53-300x49.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThere are four basic types of conic sections: parabola, circle, ellipse, and hyperbola. Each of these can be represented by the intersection of a double-napped cone and a plane. The intersections for a parabola, circle, and ellipse are shown below.Sketch the intersection for a hyperbola.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-8.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 8\" width=\"277\" height=\"149\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe graph of the rational function f is a hyperbola. The asymptotes of the graph of f intersect at (3, 2). The point (2, 1) is on the graph. Find another point on the graph. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-55.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 55\" width=\"577\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-55.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-55-300x46.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nDescribe the intervals where the graph of y = \\(\\frac{a}{x}\\) is increasing or decreasing when (a) a &gt; 0 and (b) a &lt; 0. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nAn Internet service provider charges a $50 installation fee and a monthly fee of $43. The table shows the average monthly costs y of a competing provider for x months of service. Under what conditions would a person choose one provider over the other? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-9.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 9\" width=\"275\" height=\"169\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-57.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 57\" width=\"546\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-57.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-57-300x74.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe Doppler effect occurs when the source of a sound is moving relative to a listener, so that the frequency f<sub>\u2113<\/sub>(in hertz) heard by the listener is different from the frequency f<sub>s<\/sub>(in hertz) at the source. In both equations below, r is the speed (in miles per hour) of the sound source.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-10.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 10\" width=\"309\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-10.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-10-300x152.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\na. An ambulance siren has a frequency of 2000 hertz. Write two equations modeling the frequencies heard when the ambulance is approaching and when the ambulance is moving away.<br \/>\nb. Graph the equations in part (a) using the domain 0 \u2264 r \u2264 60.<br \/>\nc. For any speed r, how does the frequency heard for an approaching sound source compare with the frequency heard when the source moves away?<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 59.<br \/>\n4x<sup>2<\/sup> \u2212 4x\u2212 80<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-59.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 59\" width=\"334\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-59.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-59-300x58.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 60.<br \/>\n3x<sup>2<\/sup> \u2212 3x \u2212 6<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n2x<sup>2<\/sup> \u2212 2x \u2212 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-61.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 61\" width=\"319\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-61.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-61-300x63.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p>Question 62.<br \/>\n10x<sup>2<\/sup> + 31x \u2212 14<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 63.<br \/>\n3<sup>2<\/sup> \u2022 3<sup>4<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-63.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 63\" width=\"207\" height=\"32\" \/><\/p>\n<p>Question 64.<br \/>\n2<sup>1\/2<\/sup> \u2022 2<sup>3\/5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n\\(\\frac{6^{5 \/ 6}}{6^{1 \/ 6}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-a-65.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 a 65\" width=\"246\" height=\"54\" \/><\/p>\n<p>Question 66.<br \/>\n\\(\\frac{6^{8}}{6^{10}}\\)<br \/>\nAnswer:<\/p>\n<h3><a id=\"Rational_Functions_Study_Skills:_Analyzing_Your_Errors\"><\/a>Rational Functions Study Skills: Analyzing Your Errors<\/h3>\n<p><strong>7.1\u20137.2 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\ninverse variation, p. 360<br \/>\nconstant of variation, p. 360<br \/>\nrational function, p. 366<\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 7.1<br \/>\nInverse Variation, p. 360<br \/>\nWriting Inverse Variation Equations, p. 361<\/p>\n<p>Section 7.2<br \/>\nParent Function for Simple Rational Functions, p. 366<br \/>\nGraphing Translations of Simple Rational Functions, p. 367<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nExplain the meaning of the given information in Exercise 25 on page 364.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow are you able to recognize whether the logic used in Exercise 29 on page 364 is correct or flawed?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow can you evaluate the reasonableness of your answer in part (b) of Exercise 41 on page 371?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nHow did the context allow you to determine a reasonable domain and range for the function in Exercise 46 on page 371?<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: AnalyzingYour Errors<\/strong><\/p>\n<p>Study Errors<br \/>\nWhat Happens: You do not study the right material or you do not learn it well enough to remember it on a test without resources such as notes.<br \/>\nHow to Avoid This Error: Take a practice test. Work with a study group. Discuss the topics on the test with your teacher. Do not try to learn a whole chapter\u2019s worth of material in one night.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-11.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions 7.2 11\" width=\"367\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-11.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-7.2-11-300x219.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><\/p>\n<h3><a id=\"Rational_Functions_7.1\u20137.2_Quiz\"><\/a>Rational Functions 7.1\u20137.2 Quiz<\/h3>\n<p><strong>Tell whether x and y show direct variation, inverse variation, or neither. Explain your reasoning.<\/strong><br \/>\nQuestion 1.<br \/>\nx + y = 7<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{5}\\)x = y<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nxy = 0.45&#8242;<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions q 1\" width=\"199\" height=\"75\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-2.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions q 2\" width=\"202\" height=\"71\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions q 3\" width=\"203\" height=\"75\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nThe variables x and y vary inversely, and y= 10 when x= 5. Write an equation that relates x and y. Then find y when x = \u22122.<br \/>\nAnswer:<\/p>\n<p><strong>Match the equation with the correct graph. Explain your reasoning.<\/strong><br \/>\nQuestion 8.<br \/>\nf(x) = \\(\\frac{3}{x}\\) + 2<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = \\(\\frac{-2}{x+3}\\) \u2212 2<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nh(x) = \\(\\frac{2x+2}{3x+1}\\)<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-38898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions q 4\" width=\"671\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-4.png 671w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-4-300x61.png 300w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><\/p>\n<p>Question 11.<br \/>\nRewrite g(x) = \\(\\frac{2x+9}{x+8}\\) in the form g(x) = \\(\\frac{a}{x-h}\\). Graph the function. Describe the graph of g as a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nThe time t (in minutes) required to empty a tank varies inversely with the pumping rate r (in gallons per minute). The rate of a certain pump is 70 gallons per minute. It takes the pump 20 minutes to empty the tank. Complete the table for the times it takes the pump to empty a tank for the given pumping rates.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions q 5\" width=\"231\" height=\"179\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nA pitcher throws 16 strikes in the first 38 pitches. The table shows how a pitcher\u2019s strike percentage changes when the pitcher throws x consecutive strikes after the first 38 pitches. Write a rational function for the strike percentage in terms of x. Graph the function. How many consecutive strikes must the pitcher throw to reach a strike percentage of 0.60?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions q 6\" width=\"550\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-6.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-q-6-300x118.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_7.3_Multiplying_and_Dividing_Rational_Expressions\"><\/a>Lesson 7.3 Multiplying and Dividing Rational Expressions<\/h3>\n<p><strong>Essential Question<\/strong> How can you determine the excluded values in a product or quotient of two rational expressions?<br \/>\nYou can multiply and divide rational expressions in much the same way that you multiply and divide fractions. Values that make the denominator of an expression zero are excluded values<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 1\" width=\"470\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-1.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-1-300x58.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Multiplying and Dividing Rational Expressions<br \/>\nWork with a partner. Find the product or quotient of the two rational expressions. Then match the product or quotient with its excluded values. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-2.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 2\" width=\"379\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-2.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-2-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-2-150x150.png 150w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing a Product or Quotient<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 3\" width=\"225\" height=\"173\" \/><br \/>\nWork with a partner. Write a product or quotient of rational expressions that has the given excluded values. Justify your answer.<br \/>\na. \u22121<br \/>\nb. \u22121 and 3<br \/>\nc. \u22121, 0, and 3<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you determine the excluded values in a product or quotient of two rational expressions?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nIs it possible for the product or quotient of two rational expressions to have no excluded values? Explain your reasoning. If it is possible, give an example.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Simplify the rational expression, if possible.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{2(x+1)}{(x+1)(x+3)}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{x+4}{x^{2}-16}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4}{x(x+2)}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{x^{2}-2 x-3}{x^{2}-x-6}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\frac{3 x^{5} y^{2}}{8 x y} \\cdot \\frac{6 x y^{2}}{9 x^{3} y}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{2 x^{2}-10 x}{x^{2}-25} \\cdot \\frac{x+3}{2 x^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{x+5}{x^{3}-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\) \u2022 (x<sup>2<\/sup> + x + 1)<br \/>\nAnswer:<\/p>\n<p><strong>Find the quotient.<\/strong><br \/>\nQuestion 9.<br \/>\n\\(\\frac{4 x}{5 x-20} \\div \\frac{x^{2}-2 x}{x^{2}-6 x+8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{2 x^{2}+3 x-5}{6 x}\\) \u00f7 (2x<sup>2<\/sup> + 5x)<br \/>\nAnswer:<\/p>\n<h3><a id=\"Multiplying_and_Dividing_Rational_Expressions_7.3_Exercises\"><\/a>Multiplying and Dividing Rational Expressions 7.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how to multiply and divide two rational expressions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-1.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 1\" width=\"566\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-1.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-1-300x76.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich rational expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-4.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 4\" width=\"473\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-4.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-4-300x38.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, simplify the expression, if possible.<\/strong><br \/>\nQuestion 3.<br \/>\n\\(\\frac{2 x^{2}}{3 x^{2}-4 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-3.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 3\" width=\"255\" height=\"110\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{7 x^{3}-x^{2}}{2 x^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{x^{2}-3 x-18}{x^{2}-7 x+6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 5\" width=\"309\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-5.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-5-300x109.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{x^{2}+13 x+36}{x^{2}-7 x+10}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{x^{2}+11 x+18}{x^{3}+8}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 7\" width=\"385\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-7.png 385w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-7-300x89.png 300w\" sizes=\"(max-width: 385px) 100vw, 385px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{x^{2}-7 x+12}{x^{3}-27}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{32 x^{4}-50}{4 x^{3}-12 x^{2}-5 x+15}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 9\" width=\"460\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-9.png 460w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-9-300x78.png 300w\" sizes=\"(max-width: 460px) 100vw, 460px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3 x^{3}-3 x^{2}+7 x-7}{27 x^{4}-147}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u201320, find the product.<\/strong><br \/>\nQuestion 11.<br \/>\n\\(\\frac{4 x y^{3}}{x^{2} y} \\cdot \\frac{y}{8 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 11\" width=\"237\" height=\"114\" \/><\/p>\n<p>Question 12.<br \/>\n\\(\\frac{48 x^{5} y^{3}}{y^{4}} \\cdot \\frac{x^{2} y}{6 x^{3} y^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{x^{2}(x-4)}{x-3} \\cdot \\frac{(x-3)(x+6)}{x^{3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 13\" width=\"515\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-13.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-13-300x68.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\frac{x^{3}(x+5)}{x-9} \\cdot \\frac{(x-9)(x+8)}{3 x^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{x^{2}-3 x}{x-2} \\cdot \\frac{x^{2}+x-6}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 15\" width=\"518\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-15.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-15-300x89.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 16.<br \/>\n\\(\\frac{x^{2}-4 x}{x-1} \\cdot \\frac{x^{2}+3 x-4}{2 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{x^{2}+3 x-4}{x^{2}+4 x+4} \\cdot \\frac{2 x^{2}+4 x}{x^{2}-4 x+3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-17.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 17\" width=\"565\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-17.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-17-300x94.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{x^{2}-x-6}{4 x^{3}} \\cdot \\frac{2 x^{2}+2 x}{x^{2}+5 x+6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{x^{2}+5 x-36}{x^{2}-49}\\) \u2022 (x<sup>2<\/sup> &#8211; 11x + 28)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-19.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 19\" width=\"339\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-19.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-19-300x205.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{x^{2}-x-12}{x^{2}-16}\\) \u2022 (x<sup>2<\/sup> &#8211; 2x + 8)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in simplifying the rational expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-5.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 5\" width=\"321\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-5.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-5-300x105.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-21.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 21\" width=\"544\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-21.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-21-300x97.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the product.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-6.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 6\" width=\"327\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-6.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-6-300x124.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWhich rational expression is in simplified form?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-7.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 7\" width=\"295\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-23.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 23\" width=\"452\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-23.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-23-300x25.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nFind the product below by multiplying the numerators and denominators, then simplifying. Then find the product by simplifying each expression, then multiplying. Which method do you prefer? Explain.<br \/>\n\\(\\frac{4 x^{2} y}{2 x^{3}} \\cdot \\frac{12 y^{4}}{24 x^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the function f(x) = \\(\\frac{(3 x-7)(x+6)}{(3 x-7)}\\) to the function g(x) = x + 6.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-25.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 25\" width=\"587\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-25.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-25-300x51.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nWrite a model in terms of x for the total area of the base of the building.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-8.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 8\" width=\"320\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-8.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-8-300x143.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 27\u201334, find the quotient.<\/strong><br \/>\nQuestion 27.<br \/>\n\\(\\frac{32 x^{3} y}{y^{8}} \\div \\frac{y^{7}}{8 x^{4}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-27.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 27\" width=\"290\" height=\"177\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\frac{2 x y z}{x^{3} z^{3}} \\div \\frac{6 y^{4}}{2 x^{2} z^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n\\(\\frac{x^{2}-x-6}{2 x^{4}-6 x^{3}} \\div \\frac{x+2}{4 x^{3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-29.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 29\" width=\"452\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-29.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-29-300x137.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 30.<br \/>\n\\(\\frac{2 x^{2}-12 x}{x^{2}-7 x+6} \\div \\frac{2 x}{3 x-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n\\(\\frac{x^{2}-x-6}{x+4}\\) \u00f7 (x<sup>2<\/sup> &#8211; 6x + 9)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-31.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 31\" width=\"566\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-31.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-31-300x123.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 32.<br \/>\n\\(\\frac{x^{2}-5 x-36}{x+2}\\) \u00f7 (x<sup>2<\/sup> &#8211; 18x + 81)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n\\(\\frac{x^{2}+9 x+18}{x^{2}+6 x+8} \\div \\frac{x^{2}-3 x-18}{x^{2}+2 x-8}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-33.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 33\" width=\"354\" height=\"288\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-33.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-33-300x244.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<p>Question 34.<br \/>\n\\(\\frac{x^{2}-3 x-40}{x^{2}+8 x-20} \\div \\frac{x^{2}+13 x+40}{x^{2}+12 x+20}\\)<br \/>\nAnswer:<\/p>\n<p>In Exercises 35 and 36, use the following information. Manufacturers often package products in a way that uses the least amount of material. One measure of the efficiency of a package is the ratio of its surface area S to its volume V. The smaller the ratio, the more efficient the packaging.<br \/>\nQuestion 35.<br \/>\nYou are examining three cylindrical containers.<br \/>\na. Write an expression for the efficiency ratio \\(\\frac{S}{V}\\) of a cylinder.<br \/>\nb. Find the efficiency ratio for each cylindrical can listed in the table. Rank the three cans according to efficiency.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-9.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 9\" width=\"310\" height=\"104\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-9.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-9-300x101.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-35.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 35\" width=\"586\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-35.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-35-300x196.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA popcorn company is designing a new tin with the same square base and twice the height of the old tin.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-10.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 10\" width=\"179\" height=\"192\" \/><br \/>\na. Write an expression for the efficiency ratio \\(\\frac{S}{V}\\) of each tin.<br \/>\nb. Did the company make a good decision by creating the new tin? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe total amount I (in millions of dollars) of healthcare expenditures and the residential population P (in millions) in the United States can be modeled by<br \/>\nI = \\(\\frac{171,000 t+1,361,000}{1+0.018 t}\\) and P = 2.96t + 278.649<br \/>\nwhere t is the number of years since 2000. Find a model M for the annual healthcare expenditures per resident. Estimate the annual healthcare expenditures per resident in 2010.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-37.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 37\" width=\"574\" height=\"506\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-37.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-37-300x264.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe total amount I (in millions of dollars) of school expenditures from prekindergarten to a college level and the enrollment P(in millions) in prekindergarten through college in the United States can be modeled by<br \/>\nI = \\(\\frac{17.913 t+709,569}{1-0.028 t}\\) and P = 0.5906t + 70.219<br \/>\nwhere t is the number of years since 2001. Find a model M for the annual education expenditures per student. Estimate the annual education expenditures per student in 2009.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-11.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 11\" width=\"249\" height=\"158\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nRefer to the population model P in Exercise 37.<br \/>\na. Interpret the meaning of the coefficient of t.<br \/>\nb. Interpret the meaning of the constant term.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-39.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 39\" width=\"562\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-39.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-39-300x51.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graphs of f and g to determine the excluded values of the functions h(x) = (fg)(x) and k(x) = (\\(\\frac{f}{g}\\)) (x). Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-12.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 12\" width=\"286\" height=\"136\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nComplete the table for the function y = \\(\\frac{x+4}{x^{2}-16}\\) . Then use the trace feature of a graphing calculator to explain the behavior of the function at x = \u22124.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-13.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 13\" width=\"170\" height=\"185\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-41.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 41\" width=\"538\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-41.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-41-300x187.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou and your friend are asked to state the domain of the expression below.<br \/>\n\\(\\frac{x^{2}+6 x-27}{x^{2}+4 x-45}\\)<br \/>\nYour friend claims the domain is all real numbers except 5. You claim the domain is all real numbers except \u22129 and 5. Who is correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind the ratio of the perimeter to the area of the triangle shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-14.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 14\" width=\"234\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-43.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 43\" width=\"611\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-43.png 611w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-43-300x181.png 300w\" sizes=\"(max-width: 611px) 100vw, 611px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nFind the expression that makes the following statement true. Assume x \u2260 \u22122 and x \u2260 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-15.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 15\" width=\"275\" height=\"57\" \/><br \/>\nans;<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 45 and 46, perform the indicated operations.<br \/>\nQuestion 45.<br \/>\n\\(\\frac{2 x^{2}+x-15}{2 x^{2}-11 x-21}\\) \u2022 (6x + 9) \u00f7 \\(\\frac{2 x-5}{3 x-21}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-45.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 45\" width=\"399\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-45.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-45-300x211.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 46.<br \/>\n(x<sup>3<\/sup> + 8) \u2022 \\(\\frac{x-2}{x^{2}-2 x+4} \\div \\frac{x^{2}-4}{x-6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>REASONING<\/strong><br \/>\nAnimals that live in temperatures several degrees colder than their bodies must avoid losing heat to survive. Animals can better conserve body heat as their surface area to volume ratios decrease. Find the surface area to volume ratio of each penguin shown by using cylinders to approximate their shapes. Which penguin is better equipped to live in a colder environment? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-16.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 16\" width=\"279\" height=\"193\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-47.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 47\" width=\"594\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-47.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-47-300x125.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs it possible to write two radical functions whose product when graphed is a parabola and whose quotient when graphed is a hyperbola? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind two rational functions f and g that have the stated product and quotient.<br \/>\n(fg)(x) = x<sup>2<\/sup>, (\\(\\left(\\frac{f}{g}\\right)\\)) (x) = \\(\\frac{(x-1)^{2}}{(x+2)^{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-49.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 49\" width=\"434\" height=\"437\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-49.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-49-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-49-150x150.png 150w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 50.<br \/>\n\\(\\frac{1}{2}\\)x + 4 = \\(\\frac{3}{2}\\)x + 5<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n\\(\\frac{1}{3}\\)x \u2212 2 = \\(\\frac{3}{4}\\)x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-51.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 51\" width=\"157\" height=\"143\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\frac{1}{4}\\)x \u2212 \\(\\frac{3}{5}\\) = \\(\\frac{9}{2}\\)x \u2212 \\(\\frac{4}{5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\\(\\frac{1}{2}\\)x + \\(\\frac{1}{3}\\) = \\(\\frac{3}{4}\\)x \u2212 \\(\\frac{1}{5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-53.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 53\" width=\"221\" height=\"143\" \/><\/p>\n<p><strong>Write the prime factorization of the number. If the number is prime, then write prime.<\/strong><br \/>\nQuestion 54.<br \/>\n42<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n91<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-54.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 54\" width=\"167\" height=\"26\" \/><\/p>\n<p>Question 56.<br \/>\n72<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n79<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Solutions-Chapter-7-Rational-Functions-7.3-a-57.png\" alt=\"Big Ideas Math Algebra 2 Solutions Chapter 7 Rational Functions 7.3 a 57\" width=\"140\" height=\"33\" \/><\/p>\n<h3><a id=\"Lesson_7.4_Adding_and_Subtracting_Rational_Expressions\"><\/a>Lesson 7.4 Adding and Subtracting Rational Expressions<\/h3>\n<p><strong>Essential Question<\/strong><br \/>\nHow can you determine the domain of the sum or difference of two rational expressions?<br \/>\nYou can add and subtract rational expressions in much the same way that you add and subtract fractions.<br \/>\n\\(\\frac{x}{x+1}+\\frac{2}{x+1}=\\frac{x+2}{x+1}\\) Sum of rational expressions<br \/>\n\\(\\frac{1}{x}-\\frac{1}{2 x}=\\frac{2}{2 x}-\\frac{1}{2 x}=\\frac{1}{2 x}\\) Difference of rational expressions<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Adding and Subtracting Rational Expressions<br \/>\nWork with a partner. Find the sum or difference of the two rational expressions. Then match the sum or difference with its domain. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 1\" width=\"502\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-1.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-1-300x230.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing a Sum or Difference<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 2\" width=\"223\" height=\"171\" \/><br \/>\nWork with a partner. Write a sum or difference of rational expressions that has the given domain. Justify your answer.<br \/>\na. all real numbers except \u22121<br \/>\nb. all real numbers except \u22121 and 3<br \/>\nc. all real numbers except \u22121, 0, and 3<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you determine the domain of the sum or difference of two rational expressions?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nYour friend found a sum as follows. Describe and correct the error(s).<br \/>\n\\(\\frac{x}{x+4}+\\frac{3}{x-4}=\\frac{x+3}{2 x}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Find the sum or difference.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{8}{12 x}-\\frac{5}{12 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{2}{3 x^{2}}+\\frac{1}{3 x^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4 x}{x-2}-\\frac{x}{x-2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{2 x^{2}}{x^{2}+1}+\\frac{2}{x^{2}+1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nFind the least common multiple of 5x<sup>3<\/sup> and 10x<sup>2<\/sup> \u2212 15x.<br \/>\nAnswer:<\/p>\n<p><strong>Find the sum or difference.<\/strong><br \/>\nQuestion 6.<br \/>\n\\(\\frac{3}{4 x}-\\frac{1}{7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{3 x^{2}}+\\frac{x}{9 x^{2}-12}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{x}{x^{2}-x-12}+\\frac{5}{12 x-48}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nRewrite g(x) = \\(\\frac{2 x-4}{x-3}\\) in the form g(x) = \\(\\frac{a}{x-h}\\) + k. Graph the function. Describe the graph of g as a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the complex fraction.<\/strong><br \/>\nQuestion 10.<br \/>\n\\(\\frac{\\frac{x}{6}-\\frac{x}{3}}{\\frac{x}{5}-\\frac{7}{10}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{\\frac{2}{x}-4}{\\frac{2}{x}+3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{\\frac{3}{x+5}}{\\frac{2}{x-3}+\\frac{1}{x+5}}\\)<br \/>\nAnswer:<\/p>\n<h3><a id=\"Adding_and_Subtracting_Rational_Expressions_7.4_Exercises\"><\/a>Adding and Subtracting Rational Expressions 7.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nA fraction that contains a fraction in its numerator or denominator is called a(n) __________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 1\" width=\"495\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-1.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-1-300x38.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how adding and subtracting rational expressions is similar to adding and subtracting numerical fractions.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, find the sum or difference.<\/strong><br \/>\nQuestion 3.<br \/>\n\\(\\frac{15}{4 x}+\\frac{5}{4 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 3\" width=\"292\" height=\"60\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{x}{16 x^{2}}-\\frac{4}{16 x^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{9}{x+1}-\\frac{2 x}{x+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 5\" width=\"260\" height=\"55\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3 x^{2}}{x-8}+\\frac{6 x}{x-8}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{5 x}{x+3}+\\frac{15}{x+3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 7\" width=\"490\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-7.png 490w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-7-300x34.png 300w\" sizes=\"(max-width: 490px) 100vw, 490px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{4 x^{2}}{2 x-1}-\\frac{1}{2 x-1}\\)<\/p>\n<p><strong>In Exercises 9\u201316, find the least common multiple of the expressions.<\/strong><br \/>\nQuestion 9.<br \/>\n3x, 3(x \u2212 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 9\" width=\"569\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-9.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-9-300x52.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 10.<br \/>\n2x<sup>2<\/sup>, 4x+ 12<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n2x, 2x(x \u2212 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 11\" width=\"540\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-11.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-11-300x51.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 12.<br \/>\n24x<sup>2<\/sup>, 8x<sup>2<\/sup> \u2212 16x<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nx<sup>2<\/sup> \u2212 25, x \u2212 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 13\" width=\"559\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-13.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-13-300x102.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 14.<br \/>\n9x<sup>2<\/sup> \u2212 16, 3x<sup>2<\/sup> + x \u2212 4<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> + 3x \u2212 40, x \u2212 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 15\" width=\"568\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-15.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-15-300x101.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> \u2212 2x \u2212 63, x + 7<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 17 and 18, describe and correct the error in finding the sum.<br \/>\nQuestion 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 3\" width=\"321\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-3.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-3-300x64.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 17\" width=\"552\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-17.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-17-300x88.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 4\" width=\"327\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-4.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-4-300x62.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201326, find the sum or difference.<\/strong><br \/>\nQuestion 19.<br \/>\n\\(\\frac{12}{5 x}-\\frac{7}{6 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 19\" width=\"222\" height=\"114\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{8}{3 x^{2}}+\\frac{5}{4 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{3}{x+4}-\\frac{1}{x+6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 21\" width=\"470\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-21.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-21-300x111.png 300w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\frac{9}{x-3}+\\frac{2 x}{x+1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{12}{x^{2}+5 x-24}+\\frac{3}{x-3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-23.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 23\" width=\"543\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-23.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-23-300x128.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{x^{2}-5}{x^{2}+5 x-14}-\\frac{x+3}{x+7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{x+2}{x-4}+\\frac{2}{x}+\\frac{5 x}{3 x-1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-25.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 25\" width=\"557\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-25.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-25-300x206.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\frac{x+3}{x^{2}-25}-\\frac{x-1}{x-5}+\\frac{3}{x+3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong> In Exercises 27 and 28, tell whether the statement is always, sometimes, or never true. Explain.<br \/>\nQuestion 27.<br \/>\nThe LCD of two rational expressions is the product of the denominators.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-27.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 27\" width=\"581\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-27.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-27-300x57.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 28.<br \/>\nThe LCD of two rational expressions will have a degree greater than or equal to that of the denominator with the higher degree.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>ANALYZING EQUATIONS<\/strong><br \/>\nHow would you begin to rewrite the function g(x) = \\(\\frac{4 x+1}{x+2}\\) to obtain the form g(x) = a \\(\\frac{a}{x-h}\\) + k?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 5\" width=\"211\" height=\"148\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-29.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 29\" width=\"266\" height=\"32\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>ANALYZING EQUATIONS<\/strong><br \/>\nHow would you begin to rewrite the function g(x) = \\(\\frac{x}{x-5}\\) to obtain the form g(x) = \\(\\frac{a}{x-h}\\) + k?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 6\" width=\"218\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 31\u201338, rewrite the function g in the form g(x) = \\(\\frac{a}{x-h}\\) + k. Graph the function. Describe the graph of g as a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nQuestion 31.<br \/>\ng(x) = \\(\\frac{5 x-7}{x-1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 31\" width=\"558\" height=\"593\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-31.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-31-282x300.png 282w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 32.<br \/>\ng(x) = \\(\\frac{6 x+4}{x+5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ng(x) = \\(\\frac{12 x}{x-5}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 33\" width=\"567\" height=\"644\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-33.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-33-264x300.png 264w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 34.<br \/>\ng(x) = \\(\\frac{8 x}{x+13}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ng(x) = \\(\\frac{2 x+3}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 35\" width=\"515\" height=\"438\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-35.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-35-300x255.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 36.<br \/>\ng(x) = \\(\\frac{4 x-6}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ng(x) = \\(\\frac{3 x+11}{x-3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-37.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 37\" width=\"579\" height=\"545\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-37.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-37-300x282.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 38.<br \/>\ng(x) = \\(\\frac{7 x-9}{x+10}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 39\u201344, simplify the complex fraction.<\/strong><br \/>\nQuestion 39.<br \/>\n\\(\\frac{\\frac{x}{3}-6}{10+\\frac{4}{x}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-39.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 39\" width=\"307\" height=\"371\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-39.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-39-248x300.png 248w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 40.<br \/>\n\\(\\frac{15-\\frac{2}{x}}{\\frac{x}{5}+4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n\\(\\frac{\\frac{1}{2 x-5}-\\frac{7}{8 x-20}}{\\frac{x}{2 x-5}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-41.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 41\" width=\"434\" height=\"545\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-41.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-41-239x300.png 239w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p>Question 42.<br \/>\n\\(\\frac{\\frac{16}{x-2}}{\\frac{4}{x+1}+\\frac{6}{x}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{\\frac{1}{3 x^{2}-3}}{\\frac{5}{x+1}-\\frac{x+4}{x^{2}-3 x-4}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-43.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 43\" width=\"564\" height=\"650\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-43.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-43-260x300.png 260w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\frac{\\frac{3}{x-2}-\\frac{6}{x^{2}-4}}{\\frac{3}{x+2}+\\frac{1}{x-2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe total time T (in hours) needed to fly from New York to Los Angeles and back can be modeled by the equation below, where dis the distance (in miles) each way, a is the average airplane speed (in miles per hour), and j is the average speed (in miles per hour) of the jet stream. Simplify the equation. Then find the total time it takes to fly 2468 miles when a= 510 miles per hour and j = 115 miles per hour.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 7\" width=\"349\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-7.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-7-300x178.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-45.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 45\" width=\"392\" height=\"387\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-45.png 392w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-45-300x296.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nThe total resistance Rt of two resistors in a parallel circuit with resistances R<sub>1<\/sub> and R<sub>2<\/sub> (in ohms) is given by the equation shown. Simplify the complex fraction. Then find the total resistance when R<sub>1<\/sub> = 2000 ohms and R<sub>2<\/sub> = 5600 ohms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 8\" width=\"261\" height=\"173\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou plan a trip that involves a 40-mile bus ride and a train ride. The entire trip is 140 miles. The time (in hours) the bus travels is y<sub>1<\/sub> = \\(\\frac{40}{x}\\), where x is the average speed (in miles per hour) of the bus. The time (in hours) the train travels is y<sub>2<\/sub>= \\(\\frac{100}{x+30}\\).Write and simplify a model that shows the total time y of the trip.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-47.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 47\" width=\"291\" height=\"324\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-47.png 291w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-47-269x300.png 269w\" sizes=\"(max-width: 291px) 100vw, 291px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou participate in a sprint triathlon that involves swimming, bicycling, and running. The table shows the distances (in miles) and your average speed for each portion of the race.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 9\" width=\"309\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-9.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-9-300x141.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\na. Write a model in simplified form for the total time (in hours) it takes to complete the race.<br \/>\nb. How long does it take to complete the race if you can swim at an average speed of 2 miles per hour? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that the least common multiple of two numbers is always greater than each of the numbers. Is your friend correct? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-49.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 49\" width=\"579\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-49.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-49-300x31.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph of the function f(x) = \\(\\frac{a}{x-h}\\) + k to determine the values of h and k.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 10\" width=\"154\" height=\"161\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>REWRITING A FORMULA<\/strong><br \/>\nYou borrow P dollars to buy a car and agree to repay the loan over t years at a monthly interest rate of i (expressed as a decimal). Your monthly payment M is given by either formula below.<br \/>\nM = \\(\\frac{P i}{1-\\left(\\frac{1}{1+i}\\right)^{12 t}}\\) or M = \\(\\frac{P i(1+i)^{12 t}}{(1+i)^{12 t}-1}\\)<br \/>\na. Show that the formulas are equivalent by simplifying the first formula.<br \/>\nb. Find your monthly payment when you borrow$15,500 at a monthly interest rate of 0.5% and repay the loan over 4 years.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-51.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 51\" width=\"399\" height=\"378\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-51.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-51-300x284.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs it possible to write two rational functions whose sum is a quadratic function? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nUse technology to rewrite the function g(x) = \\(\\frac{(97.6)(0.024)+x(0.003)}{12.2+x}\\) in the form g(x) = \\(\\frac{a}{x-h}\\) + k. Describe the graph of g as a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-53.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 53\" width=\"517\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-53.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-53-300x124.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nFind an expression for the surface area of the box.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 11\" width=\"352\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-11.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-11-300x119.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are hired to wash the new cars at a car dealership with two other employees. You take an average of 40 minutes to wash a car (R<sub>1<\/sub> = 1\/40 car per minute). The second employee washes a car in x minutes. The third employee washes a car in x + 10 minutes.<br \/>\na. Write expressions for the rates that each employee can wash a car.<br \/>\nb. Write a single expression R for the combined rate of cars washed per minute by the group.<br \/>\nc. Evaluate your expression in part (b) when the second employee washes a car in 35 minutes. How many cars per hour does this represent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-55.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 55\" width=\"577\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-55.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-55-300x256.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe amount A(in milligrams) of aspirin in a person\u2019s bloodstream can be modeled by<br \/>\nA = \\(\\frac{391 t^{2}+0.112}{0.218 t^{4}+0.991 t^{2}+1}\\)<br \/>\nwhere t is the time (in hours) after one dose is taken.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 12\" width=\"343\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-12.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-12-300x96.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><br \/>\na. A second dose is taken 1 hour after the first dose. Write an equation to model the amount of the second dose in the bloodstream.<br \/>\nb. Write a model for the total amount of aspirin in the bloodstream after the second dose is taken.<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>FINDING A PATTERN<\/strong><br \/>\nFind the next two expressions in the pattern shown. Then simplify all five expressions. What value do the expressions approach?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 13\" width=\"325\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-13.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-13-300x97.png 300w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-57.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 57\" width=\"578\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-57.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-57-300x171.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the system by graphing.<\/strong><br \/>\nQuestion 58.<br \/>\ny = x<sup>2<\/sup> + 6<br \/>\ny = 3x + 4<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n2x<sup>2<\/sup> \u2212 3x \u2212 y = 0<br \/>\n\\(\\frac{5}{2}\\)x \u2212 y = \\(\\frac{9}{4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-59.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 59\" width=\"451\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-59.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-59-270x300.png 270w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p>Question 60.<br \/>\n3 = y \u2212 x<sup>2<\/sup> \u2212 x<br \/>\ny = \u2212x<sup>2<\/sup> \u2212 3x \u2212 5<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\ny= (x + 2)<sup>2<\/sup> \u2212 3<br \/>\ny = x<sup>2<\/sup> + 4x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-61.png\" alt=\"Big Ideas Math Answer Key Algebra 2 Chapter 7 Rational Functions 7.4 a 61\" width=\"545\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-61.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-2-Chapter-7-Rational-Functions-7.4-a-61-300x152.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<h3><a id=\"Lesson_7.5_Solving_Rational_Equations\"><\/a>Lesson 7.5 Solving Rational Equations<\/h3>\n<p><strong>Essential Question<\/strong> How can you solve a rational equation?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving Rational Equations<br \/>\nWork with a partner. Match each equation with the graph of its related system of equations. Explain your reasoning. Then use the graph to solve the equation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 1\" width=\"500\" height=\"519\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-1.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-1-289x300.png 289w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving Rational Equations<br \/>\nWork with a partner. Look back at the equations in Explorations 1(d) and 1(e). Suppose you want a more accurate way to solve the equations than using a graphical approach.<br \/>\na. Show how you could use a numerical approach by creating a table. For instance, you might use a spreadsheet to solve the equations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-2.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 2\" width=\"232\" height=\"163\" \/><br \/>\nb. Show how you could use an analytical approach. For instance, you might use the method you used to solve proportions.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you solve a rational equation?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the method in either Exploration 1 or 2 to solve each equation.<br \/>\na. \\(\\frac{x+1}{x-1}=\\frac{x-1}{x+1}\\)<br \/>\nb. \\(\\frac{1}{x+1}=\\frac{1}{x^{2}+1}\\)<br \/>\nc. \\(\\frac{1}{x^{2}-1}=\\frac{1}{x-1}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation by cross multiplying. Check your solution(s).<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{3}{5 x}=\\frac{2}{x-7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{-4}{x+3}=\\frac{5}{x-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{2 x+5}=\\frac{x}{11 x+8}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation by using the LCD. Check your solution(s).<\/strong><br \/>\nQuestion 4.<br \/>\n\\(\\frac{15}{x}+\\frac{4}{5}=\\frac{7}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{3 x}{x+1}-\\frac{5}{2 x}=\\frac{3}{2 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{4 x+1}{x+1}=\\frac{12}{x^{2}-1}+3\\)<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation. Check your solution(s).<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\frac{9}{x-2}+\\frac{6 x}{x+2}=\\frac{9 x^{2}}{x^{2}-4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{7}{x-1}-5=\\frac{6}{x^{2}-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nConsider the function f(x) = \\(\\frac{1}{x}\\) \u2212 2. Determine whether the inverse of f is a function. Then find the inverse.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nHow do the answers in Example 6 change when c = \\(\\frac{50 m+800}{m}\\)?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Rational_Equations_7.5_Exercises\"><\/a>Solving Rational Equations 7.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhen can you solve a rational equation by cross multiplying? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46159\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 1\" width=\"561\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-1-300x59.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nA student solves the equation \\(\\frac{4}{x-3}=\\frac{x}{x-3}\\) and obtains the solutions 3 and 4. Are either of these extraneous solutions? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, solve the equation by cross multiplying. Check your solution(s).<\/strong><br \/>\nQuestion 3.<br \/>\n\\(\\frac{4}{2 x}=\\frac{5}{x+6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46160\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 3\" width=\"418\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-3.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-3-300x219.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{9}{3 x}=\\frac{4}{x+2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{6}{x-1}=\\frac{9}{x+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46161\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 5\" width=\"444\" height=\"281\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-5.png 444w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-5-300x190.png 300w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{8}{3 x-2}=\\frac{2}{x-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{x}{2 x+7}=\\frac{x-5}{x-1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46162\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 7\" width=\"509\" height=\"432\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-7.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-7-300x255.png 300w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\frac{-2}{x-1}=\\frac{x-8}{x+1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{x^{2}-3}{x+2}=\\frac{x-3}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46163\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 9\" width=\"507\" height=\"338\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-9.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-9-300x200.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{-1}{x-3}=\\frac{x-4}{x^{2}-27}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nSo far in your volleyball practice, you have put into play 37 of the 44 serves you have attempted. Solve the equation \\(\\frac{90}{100}=\\frac{37+x}{44+x}\\) to find the number of consecutive serves you need to put into play in order to raise your serve percentage to 90%.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-3.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 3\" width=\"220\" height=\"163\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46164\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 11\" width=\"441\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-11.png 441w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-11-300x159.png 300w\" sizes=\"(max-width: 441px) 100vw, 441px\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>USING EQUATIONS<\/strong><br \/>\nSo far this baseball season, you have 12 hits out of 60 times at-bat. Solve the equation 0.360 = \\(\\frac{12+x}{60+x}\\) to find the number of consecutive hits you need to raise your batting average to 0.360.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nBrass is an alloy composed of 55% copper and 45% zinc by weight. You have 25 ounces of copper. How many ounces of zinc do you need to make brass?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46165\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 13\" width=\"551\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-13.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-13-300x154.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou have 0.2 liter of an acid solution whose acid concentration is 16 moles per liter. You want to dilute the solution with water so that its acid concentration is only 12 moles per liter. Use the given model to determine how many liters of water you should add to the solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-4.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 4\" width=\"342\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-4.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-4-300x81.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 15\u201318, identify the LCD of the rational expressions in the equation.<br \/>\nQuestion 15.<br \/>\n\\(\\frac{x}{x+3}+\\frac{1}{x}=\\frac{3}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46166\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-15.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 15\" width=\"221\" height=\"31\" \/><\/p>\n<p>Question 16.<br \/>\n\\(\\frac{5 x}{x-1}-\\frac{7}{x}=\\frac{9}{x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{2}{x+1}+\\frac{x}{x+4}=\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46167\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-17.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 17\" width=\"278\" height=\"32\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{4}{x+9}+\\frac{3 x}{2 x-1}=\\frac{10}{3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201330, solvethe equation by using the LCD. Check your solution(s).<\/strong><br \/>\nQuestion 19.<br \/>\n\\(\\frac{3}{2}+\\frac{1}{x}\\) = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46168\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-19.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 19\" width=\"416\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-19.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-19-300x148.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{2}{3 x}+\\frac{1}{6}=\\frac{4}{3 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n\\(\\frac{x-3}{x-4}\\) + 4 = \\(\\frac{3 x}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46169\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 21\" width=\"326\" height=\"599\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-21.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-21-163x300.png 163w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\frac{2}{x-3}+\\frac{1}{x}=\\frac{x-1}{x-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{6 x}{x+4}\\) + 4 = \\(\\frac{2 x+2}{x-1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46170\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 23\" width=\"518\" height=\"730\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-23.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-23-213x300.png 213w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{10}{x}\\) + 3 = \\(\\frac{x+9}{x-4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\\(\\frac{18}{x^{2}-3 x}-\\frac{6}{x-3}=\\frac{5}{x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46171\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 25\" width=\"552\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-25.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-25-300x293.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\frac{10}{x^{2}-2 x}+\\frac{4}{x}=\\frac{5}{x-2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{x+1}{x+6}+\\frac{1}{x}=\\frac{2 x+1}{x+6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46172\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 27\" width=\"411\" height=\"699\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-27.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-27-176x300.png 176w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\frac{x+3}{x-3}+\\frac{x}{x-5}=\\frac{x+5}{x-5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n\\(\\frac{5}{x}\\) &#8211; 2 = \\(\\frac{2}{x+3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 29\" width=\"487\" height=\"745\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-29.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-29-196x300.png 196w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 30.<br \/>\n\\(\\frac{5}{x^{2}+x-6}\\) = 2 + \\(\\frac{x-3}{x-2}\\)<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 31 and 32, describe and correct the error in the first step of solving the equation.<br \/>\nQuestion 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-5.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 5\" width=\"320\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-5.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-5-300x106.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 31\" width=\"491\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-31.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-31-300x103.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-6.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 6\" width=\"323\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-6.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-6-300x111.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou can paint a room in 8 hours. Working together, you and your friend can paint the room in just 5 hours.<br \/>\na. Let t be the time (in hours) your friend would take to paint the room when working alone. Copy and complete the table.<br \/>\n(Hint: (Work done) = (Work rate) \u00d7 (Time))<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-7.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 7\" width=\"314\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-7.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-7-300x102.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nb. Explain what the sum of the expressions represents in the last column. Write and solve an equation to find how long your friend would take to paint the room when working alone.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 33\" width=\"593\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-33.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-33-300x243.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou can clean a park in 2 hours. Working together, you and your friend can clean the park in just 1.2 hours.a. Let t be the time (in hours) your friend would take to clean the park when working alone. Copy and complete the table.<br \/>\n(Hint: (Work done) = (Work rate) \u00d7 (Time))<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-8.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 8\" width=\"307\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-8.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-8-300x111.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><br \/>\nb. Explain what the sum of the expressions represents in the last column. Write and solve an equation to find how long your friend would take to clean the park when working alone.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nGive an example of a rational equation that you would solve using cross multiplication and one that you would solve using the LCD. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 35\" width=\"560\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-35.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-35-300x118.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nDescribe a real-life situation that can be modeled by a rational equation. Justify your answer.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 37\u201344, determine whether the inverse of f is a function. Then find the inverse.<\/strong><br \/>\nQuestion 37.<br \/>\nf(x) = \\(\\frac{2}{x-4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 37\" width=\"550\" height=\"633\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-37.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-37-261x300.png 261w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 38.<br \/>\nf(x) = \\(\\frac{7}{x+6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nf(x) = \\(\\frac{3}{x}\\) &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 39\" width=\"571\" height=\"644\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-39.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-39-266x300.png 266w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 40.<br \/>\nf(x) = \\(\\frac{5}{x}\\) &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nf(x) = \\(\\frac{4}{11-2 x}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 41\" width=\"574\" height=\"711\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-41.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-41-242x300.png 242w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 42.<br \/>\nf(x) = \\(\\frac{8}{9+5 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nf(x) = \\(\\frac{1}{x^{2}}\\) + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 43\" width=\"578\" height=\"752\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-43.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-43-231x300.png 231w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 44.<br \/>\nf(x) = \\(\\frac{1}{x^{4}}\\) &#8211; 7<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe cost of fueling your car for 1 year can be calculated using this equation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-9.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 9\" width=\"330\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-9.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-9-300x84.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nLast year you drove9000 miles, paid $3.24 per gallon of gasoline, and spent a total of $1389 on gasoline. Find the fuel-efficiency rate of your car by (a) solving an equation, and (b) using the inverse of the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-10.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 10\" width=\"224\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 45\" width=\"525\" height=\"433\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-45.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-45-300x247.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe recommended percent p (in decimal form) of nitrogen (by volume) in the air that a diver breathes is given by p = \\(\\frac{105.07}{d+33}\\), where d is the depth (in feet) of the diver. Find the depth when the air contains 47% recommended nitrogen by (a) solving an equation, and (b) using the inverse of the function.<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 47\u201350, use a graphing calculator to solve the equation f(x) = g(x).<br \/>\nQuestion 47.<br \/>\nf(x) = \\(\\frac{2}{3}\\)x, g(x) = x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 47\" width=\"556\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-47.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-47-300x134.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = \u2212\\(\\frac{3}{5x}\\), g(x) = \u2212x<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nf(x) = \\(\\frac{1}{x}\\) + 1, g(x) = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 49\" width=\"554\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-49.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-49-300x120.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 50.<br \/>\nf(x) = \\(\\frac{2}{x}\\) + 1, g(x) = x<sup>2<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nGolden rectangles are rectangles for which the ratio of the width w to the length \u2113 is equal to the ratio of \u2113 to \u2113+w. The ratio of the length to the width for these rectangles is called the golden ratio. Find the value of the golden ratio using a rectangle with a width of 1 unit.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-11.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 11\" width=\"159\" height=\"106\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-51.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 51\" width=\"525\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-51.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-51-300x185.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nUse the graph to identify the solution(s) of the rational equation \\(\\frac{4(x-1)}{x-1}=\\frac{2 x-2}{x+1}\\). Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-12.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 12\" width=\"230\" height=\"194\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 53 and 54, find the inverse of the function. (Hint: Try rewriting the function by using either inspection or long division.)<br \/>\nQuestion 53.<br \/>\nf(x) = \\(\\frac{3 x+1}{x-4}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-53.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 53\" width=\"364\" height=\"730\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-53.png 364w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-53-150x300.png 150w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<p>Question 54.<br \/>\nf(x) = \\(\\frac{4 x-7}{2 x+3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nFind the inverse of rational functions of the form y = \\(\\frac{a x+b}{c x+d}\\). Verify your answer is correct by using it to find the inverses in Exercises 53 and 54.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 55\" width=\"570\" height=\"632\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-55.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-55-271x300.png 271w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs it possible to write a rational equation that has the following number of solutions? Justify your answers.<br \/>\na. no solution<br \/>\nb. exactly one solution<br \/>\nc. exactly two solutions<br \/>\nd. infinitely many solutions<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nLet a be a nonzero real number. Tell whether each statement is always true, sometimes true, or never true. Explain your reasoning.<br \/>\na. For the equation \\(\\frac{1}{x-a}=\\frac{x}{x-a}\\), x=a is an extraneous solution.<br \/>\nb. The equation \\(\\frac{3}{x-a}=\\frac{x}{x-a}\\) has exactly one solution.<br \/>\nc. The equation \\(\\frac{1}{x-a}=\\frac{2}{x+a}+\\frac{2 a}{x^{2}-a^{2}}\\) has no solution.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-57.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 57\" width=\"561\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-57.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-57-300x99.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that it is not possible for a rational equation of the form \\(\\frac{x-a}{b}=\\frac{x-c}{d}\\), where b\u2260 0 and d\u2260 0, to have extraneous solutions. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Is the domain discrete or continuous? Explain. Graph the function using its domain.<\/strong><br \/>\nQuestion 59.<br \/>\nThe linear function y = 0.25x represents the amount of money y (in dollars) of x quarters in your pocket. You have a maximum of eight quarters in your pocket.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-59.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 59\" width=\"573\" height=\"323\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-59.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-59-300x169.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 60.<br \/>\nA store sells broccoli for $2 per pound. The total cost t of the broccoli is a function of the number of pounds p you buy.<br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the function for the given value of x.<\/strong><br \/>\nQuestion 61.<br \/>\nf(x) = x<sup>3<\/sup> \u2212 2x + 7; x = \u22122<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-61.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 61\" width=\"307\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-61.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-61-300x94.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 62.<br \/>\ng(x) = \u22122x<sup>4<\/sup> + 7x<sup>3<\/sup> + x \u2212 2; x = 3<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\nh(x) = \u2212x<sup>3<\/sup> + 3x<sup>2<\/sup> + 5x; x = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-46190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-a-63.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 a 63\" width=\"295\" height=\"99\" \/><\/p>\n<p>Question 64.<br \/>\nk(x) = \u22122x<sup>3<\/sup> \u2212 4x<sup>2<\/sup> + 12x \u2212 5; x = \u22125<br \/>\nAnswer:<\/p>\n<h3><a id=\"Rational_Functions_Performance_Task:_Circuit_Design\"><\/a>Rational Functions Performance Task: Circuit Design<\/h3>\n<p><strong>7.3\u20137.5 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-13.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 13\" width=\"503\" height=\"54\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-13.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-13-300x32.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 7.3<br \/>\nSimplifying Rational Expressions, p. 376<br \/>\nMultiplying Rational Expressions, p. 377<br \/>\nDividing Rational Expressions, p. 378<\/p>\n<p>Section 7.4<br \/>\nAdding or Subtracting with Like Denominators, p. 384<br \/>\nAdding or Subtracting with Unlike Denominators, p. 384<br \/>\nSimplifying Complex Fractions, p. 387<\/p>\n<p>Section 7.5<br \/>\nSolving Rational Equations by Cross Multiplying, p. 392<br \/>\nSolving Rational Equations by Using the Least Common Denominator, p. 393<br \/>\nUsing Inverses of Functions, p. 395<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nIn Exercise 37 on page 381, what type of equation did you expect to get as your solution? Explain why this type of equation is appropriate in the context of this situation.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWrite a simpler problem that is similar to Exercise 44 on page 382. Describe how to use the simpler problem to gain insight into the solution of the more complicated problem in Exercise 44.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nIn Exercise 57 on page 390, what conjecture did you make about the value the given expressions were approaching? What logical progression led you to determine whether your conjecture was correct?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nCompare the methods for solving Exercise 45 on page 397. Be sure to discuss the similarities and differences between the methods as precisely as possible.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task: Circuit Design<\/strong><\/p>\n<p>A thermistor is a resistor whose resistance varies with temperature. Thermistors are an engineer\u2019s dream because they are inexpensive, small, rugged, and accurate. The one problem with thermistors is their responses to temperature are not linear. How would you design a circuit that corrects this problem?<br \/>\nTo explore the answers to these questions and more, go to BigIdeasMath.com.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-14.png\" alt=\"Big Ideas Math Answers Algebra 2 Chapter 7 Rational Functions 7.5 14\" width=\"377\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-14.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-2-Chapter-7-Rational-Functions-7.5-14-300x205.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/p>\n<h3><a id=\"Rational_Functions_Chapter_Review\"><\/a>Rational Functions Chapter Review<\/h3>\n<p><span id=\"P420_10\" class=\"s1 f44 fs99 l0\"><span id=\"P420_11\"><\/span><\/span><strong><span id=\"P420_15\" class=\"s1 f45 fs34 l6\">7.1 <\/span><span id=\"P420_12\" class=\"s1 f45 fs86 l6\">Inverse V<span id=\"P420_13\">ariation <\/span><\/span><span id=\"P420_14\" class=\"s1 f42 fs98 l0\">(pp. 359\u2013364)<\/span><\/strong><\/p>\n<p><strong>Tell whether x and y show direct variation, inverse variation, or neither.<\/strong><br \/>\nQuestion 1.<br \/>\nxy = 5<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n5y = 6x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n15 = \\(\\frac{x}{y}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ny \u2212 3 = 2x<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-cr-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions cr 5\" width=\"215\" height=\"76\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-cr-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions cr 6\" width=\"223\" height=\"78\" \/><br \/>\nAnswer:<\/p>\n<p>The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = -3.<br \/>\nQuestion 7.<br \/>\nx = 1, y = 5<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nx = \u22124, y =\u22126<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nx = \\(\\frac{5}{2}\\),y = 18<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nx = \u221212, y = \\(\\frac{2}{3}\\)<br \/>\nAnswer:<\/p>\n<p><strong>7.2 Graphing Rational Functions (pp. 365\u2013372)<\/strong><\/p>\n<p><strong>Graph the function. State the domain and range.<\/strong><br \/>\nQuestion 11.<br \/>\ny = \\(\\frac{4}{x-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\ny = \\(\\frac{1}{x+5}\\) + 2<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nf(x) = \\(\\frac{3 x-2}{x-4}\\)<br \/>\nAnswer:<\/p>\n<p><strong>7.3 Multiplying and Dividing Rational Expressions (pp. 375\u2013382)<\/strong><\/p>\n<p><strong>Find the product or quotient.<\/strong><br \/>\nQuestion 14.<br \/>\n\\(\\frac{80 x^{4}}{y^{3}} \\cdot \\frac{x y}{5 x^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{x-3}{2 x-8} \\cdot \\frac{6 x^{2}-96}{x^{2}-9}\\)<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{16 x^{2}-8 x+1}{x^{3}-7 x^{2}+12 x} \\div \\frac{20 x^{2}-5 x}{15 x^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{x^{2}-13 x+40}{x^{2}-2 x-15}\\) \u00f7 (x<sup>2<\/sup> &#8211; 5x &#8211; 24)<br \/>\nAnswer:<\/p>\n<p><strong>7.4 Adding and Subtracting Rational Expressions (pp. 383\u2013390)<\/strong><\/p>\n<p><strong>Find the sum or difference.<\/strong><br \/>\nQuestion 18.<br \/>\n\\(\\frac{5}{6(x+3)}+\\frac{x+4}{2 x}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{5 x}{x+8}+\\frac{4 x-9}{x^{2}+5 x-24}\\)<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{x+2}{x^{2}+4 x+3}-\\frac{5 x}{x^{2}-9}\\)<br \/>\nAnswer:<\/p>\n<p>Rewrite the function in the form g(x) = \\(\\frac{a}{x-h}\\) h + k. Graph the function. Describe the graph of gas a transformation of the graph of f(x) = \\(\\frac{a}{x}\\).<br \/>\nQuestion 21.<br \/>\ng(x) = \\(\\frac{5 x+1}{x-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\ng(x) = \\(\\frac{4 x+2}{x+7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ng(x) = \\(\\frac{9 x-10}{x-1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nLet f be the focal length of a thin camera lens, p be the distance between the lens and an object being photographed, and q be the distance between the lens and the film. For the photograph to be in focus, the variables should satisfy the lens equation to the right. Simplify the complex fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-cr-24.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions cr 24\" width=\"123\" height=\"95\" \/><br \/>\nAnswer:<\/p>\n<p><strong>7.5 Solving Rational Equations (pp. 391\u2013398)<\/strong><\/p>\n<p><strong>Solve the equation. Check your solution(s).<\/strong><br \/>\nQuestion 25.<br \/>\n\\(\\frac{5}{x}=\\frac{7}{x+2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n\\(\\frac{8(x-1)}{x^{2}-4}=\\frac{4}{x+2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n\\(\\frac{2(x+7)}{x+4}\\) &#8211; 2 = \\(\\frac{2 x+20}{2 x+8}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Determine whether the inverse of f is a function. Then find the inverse.<\/strong><br \/>\nQuestion 28.<br \/>\nf(x) = \\(\\frac{3}{x+6}\\)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nf(x) = \\(\\frac{10}{x-7}\\)<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\nf(x) = \\(\\frac{1}{x}\\) + 8<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nAt a bowling alley, shoe rentals cost $3 and each game costs $4. The average cost c (in dollars) of bowlingn games is given by c = \\(\\frac{4 n+3}{n}\\). Find how many games you must bowl for the average cost to fall to $4.75 by (a) solving an equation, and (b) using the inverse of a function.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Rational_Functions_Chapter_Test\"><\/a>Rational Functions Chapter Test<\/h3>\n<p>The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 4.<br \/>\nQuestion 1.<br \/>\nx = 5, y = 2<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx = \u22124, y = \\(\\frac{7}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx = \\(\\frac{3}{4}\\), y = \\(\\frac{5}{8}\\)<br \/>\nAnswer:<\/p>\n<p>The graph shows the function y = \\(\\frac{1}{x-h}\\) + k. Determine whether the value of each constant h and k is positive, negative, or zero. Explain your reasoning.<br \/>\nQuestion 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-4.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions ct 4\" width=\"159\" height=\"161\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-5.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions ct 5\" width=\"160\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-6.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions ct 6\" width=\"156\" height=\"163\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Perform the indicated operation.<\/strong><br \/>\nQuestion 7.<br \/>\n\\(\\frac{3 x^{2} y}{4 x^{3} y^{5}} \\div \\frac{6 y^{2}}{2 x y^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{3 x}{x^{2}+x-12}-\\frac{6}{x+4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{x^{2}-3 x-4}{x^{2}-3 x-18} \\cdot \\frac{x-6}{x+1}\\)<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{4}{x+5}+\\frac{2 x}{x^{2}-25}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nLet g(x) = \\(\\frac{(x+3)(x-2)}{x+3}\\). Simplify g(x). Determine whether the graph of f(x) =x\u2212 2 and the graph of g are different. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nYou start a small beekeeping business. Your initial costs are $500 for equipment and bees. You estimate it will cost $1.25 per pound to collect, clean, bottle, and label the honey. How many pounds of honey must you produce before your average cost per pound is $1.79? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nYou can use a simple lever to lift a 300-pound rock. The force F (in foot-pounds) needed to lift the rock is inversely related to the distance d (in feet) from the pivot point of the lever. To lift the rock, you need 60 pounds of force applied to a lever with a distance of 10 feet from the pivot point. What force is needed when you increase the distance to 15\ue031feet from the pivot point? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-13.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions ct 13\" width=\"351\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-13.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-13-300x155.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nThree tennis balls fit tightly in a can as shown.<br \/>\na. Write an expression for the height h of the can in terms of its radius r. Then rewrite the formula for the volume of a cylinder in terms of r only.<br \/>\nb. Find the percent of the can\u2019s volume that is not occupied by tennis balls.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answer-Key-Chapter-7-Rational-Functions-ct-14.png\" alt=\"Big Ideas Math Algebra 2 Answer Key Chapter 7 Rational Functions ct 14\" width=\"119\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Rational_Functions_Cumulative_Assessment\"><\/a>Rational Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nWhich of the following functions are shown in the graph? Select all that apply. Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-1.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions ca 1\" width=\"478\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-1.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-1-300x118.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYou step onto an escalator and begin descending. After riding for 12 feet, you realize that you dropped your keys on the upper floor and walk back up the escalator to retrieve them. The total time T of your trip down and up the escalator is given by<br \/>\nT = \\(\\frac{12}{s}+\\frac{12}{w-s}\\)<br \/>\nwhere s is the speed of the escalator and w is your walking speed. The trip took 9 seconds, and you walk at a speed of 6 feet per second. Find two possible speeds of the escalator.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe graph of a rational function has asymptotes that intersect at the point (4, 3). Choose the correct values to complete the equation of the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-3.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions ca 3\" width=\"281\" height=\"169\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe tables below give the amounts A (in dollars) of money in two different bank accounts over time t (in years).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-4.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions ca 4\" width=\"499\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-4.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-4-300x64.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\na. Determine the type of function represented by the data in each table.<br \/>\nb. Provide an explanation for the type of growth of each function.<br \/>\nc. Which account has a greater value after 10 years? after 15 years? Justify your answers.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nOrder the expressions from least to greatest. Justify your answer.(HSN-RN.A.1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-5.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions ca 5\" width=\"185\" height=\"193\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nA movie grosses $37 million after the first week of release. The weekly gross sales y decreases by 30% each week. Write an exponential decay function that represents the weekly gross sales in week x. What is a reasonable domain and range in this situation? Explain your reasoning.(HSF-LE.A.2)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nChoose the correct relationship among the variables in the table. Justify your answer by writing an equation that relates p, q, and r. (HSA-CED.A.2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-ca-6.png\" alt=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions ca 6\" width=\"118\" height=\"213\" \/><br \/>\nA. The variable p varies directly with the difference of q and r.<br \/>\nB. The variable r varies inversely with the difference of p and q.<br \/>\nC. The variable q varies inversely with the sum of p and r.<br \/>\nD. The variable p varies directly with the sum of q and r.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nYou have taken five quizzes in your history class, and your average score is 83 points. You think you can score 95 points on each remaining quiz. How many quizzes do you need to take to raise your average quiz score to 90 points? Justify your answer. (HSA-REI.A.2)<br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here, on this page, we have shared the ultimate preparation guide for high school students on algebra 2 math concepts. The given material is Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions. You can access and download BIM Algebra 2 Ch 7 Answer key for free of cost. So, it helps you to &#8230; <a title=\"Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-2-answers-chapter-7\/\" aria-label=\"More on Big Ideas Math Algebra 2 Answers Chapter 7 Rational Functions\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89293,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-2-Answers-Chapter-7-Rational-Functions-1.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/38865"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=38865"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/38865\/revisions"}],"predecessor-version":[{"id":90326,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/38865\/revisions\/90326"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89293"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=38865"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=38865"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=38865"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}