{"id":6517,"date":"2022-03-26T18:42:23","date_gmt":"2022-03-26T13:12:23","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6517"},"modified":"2022-04-07T12:48:00","modified_gmt":"2022-04-07T07:18:00","slug":"go-math-grade-8-answer-key-chapter-6-functions","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-6-functions\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 6 Functions"},"content":{"rendered":"<p>The solutions of Go Math Grade 8 Answer Key Chapter 6 Functions are provided in the pdf format here. HMH Go Math Grade 8 Answer Key Chapter 6 Functions are presented by the professional math experts in an easy manner and with brief explanations. You can find different ways of solving the problems on this page. So, we suggest the students to refer to <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> Chapter 6 Functions now to begin your practice.<\/p>\n<h2>Go Math Grade 8 Chapter 6 Functions Answer Key<\/h2>\n<p>Test and improve your knowledge by using Go Math Grade 8 Chapter 6 Functions Solution Key. The Go Math Grade 8 Chapter 6 Functions Answer Key consists of the topics like Identifying and representing functions, describing functions, analyzing graphs, etc. Use HMH Go Math Grade 8 Answer Key for the best practice of maths. After completion of your preparation test yourself by solving the problems given in the model quiz.<\/p>\n<p><strong>Lesson 1: Identifying and Representing Functions\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Identifying_and_Representing_Functions_\u2013_Page_No._158\">Identifying and Representing Functions \u2013 Page No. 158<\/a><\/li>\n<li><a href=\"#\u00b7_Identifying_and_Representing_Functions_\u2013_Page_No._159\">Identifying and Representing Functions \u2013 Page No. 159<\/a><\/li>\n<li><a href=\"#\u00b7_Identifying_and_Representing_Functions_\u2013_Page_No._160\">Identifying and Representing Functions \u2013 Page No. 160<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Describing Functions<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Describing_Functions_\u2013_Page_No._164\">Describing Functions \u2013 Page No. 164<\/a><\/li>\n<li><a href=\"#\u00b7_Describing_Functions_\u2013_Page_No._165\">Describing Functions \u2013 Page No. 165<\/a><\/li>\n<li><a href=\"#\u00b7_Describing_Functions_\u2013_Page_No._166\">Describing Functions \u2013 Page No. 166<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Comparing Functions\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Comparing_Functions_\u2013_Page_No._170\">Comparing Functions \u2013 Page No. 170<\/a><\/li>\n<li><a href=\"#\u00b7_Comparing_Functions_\u2013_Page_No._171\">Comparing Functions \u2013 Page No. 171<\/a><\/li>\n<li><a href=\"#\u00b7_Comparing_Functions_\u2013_Page_No._172\">Comparing Functions \u2013 Page No. 172<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Analyzing Graphs<\/strong><\/p>\n<ul>\n<li><a href=\"#Analyzing_Graphs_\u2013_Page_No._176\">Analyzing Graphs \u2013 Page No. 176<\/a><\/li>\n<li><a href=\"#\u00b7_Analyzing_Graphs_\u2013_Page_No._177\">Analyzing Graphs \u2013 Page No. 177<\/a><\/li>\n<li><a href=\"#\u00b7_Analyzing_Graphs_\u2013_Page_No._178\">Analyzing Graphs \u2013 Page No. 178<\/a><\/li>\n<\/ul>\n<p><strong>Model Quiz\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Model_Quiz_\u2013_Page_No._179\">Model Quiz \u2013 Page No. 179<\/a><\/li>\n<\/ul>\n<p><strong>Mixed Review\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#\u00b7_Mixed_Review_\u2013_Page_No._180\">Mixed Review \u2013 Page No. 180<\/a><\/li>\n<\/ul>\n<h3><a id=\"\u00b7_Identifying_and_Representing_Functions_\u2013_Page_No._158\"><\/a>Guided Practice &#8211; Identifying and Representing Functions &#8211; Page No. 158<\/h3>\n<p><strong>Complete each table. In the row with x as the input, write a rule as an algebraic expression for the output. Then complete the last row of the table using the rule.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 1\" width=\"192\" height=\"272\" \/><br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-1.png\" alt=\"Grade 8 Chapter 6 image 1\" width=\"252\" height=\"205\" \/><\/p>\n<p>Explanation:<br \/>\nUnit Cost of ticket = 40\/2 = 20<br \/>\nTotal cost = 20x where x is the number of tickets.<br \/>\nx = 20x<br \/>\n10 = 20(100) = 200<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 2\" width=\"189\" height=\"270\" \/><br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-2.png\" alt=\"Grade 8 Chapter 6 image 2\" width=\"247\" height=\"205\" \/><\/p>\n<p>Explanation:<br \/>\nNumber of pages per minute = 1\/2 = 0.5<br \/>\nTotal cost = 0.5x where x is the number of minutes.<br \/>\nx = 0.5x<br \/>\n30 = 0.5(30) = 15<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 3\" width=\"187\" height=\"269\" \/><br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-3.png\" alt=\"Grade 8 Chapter 6 image 3\" width=\"255\" height=\"206\" \/><\/p>\n<p>Explanation:<br \/>\nUnits cost of Muffins = 2.25\/1 = 2.25<br \/>\nTotal cost = 2.25x where x is the number of muffins<br \/>\nx = 2.25x<br \/>\n12 = 2.25(12) = 27<\/p>\n<p><strong>Determine whether each relationship is a function.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 4\" width=\"159\" height=\"103\" \/><br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nFunction<\/p>\n<p>Explanation:<br \/>\nEach input is assigned to exactly one output.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 5\" width=\"188\" height=\"175\" \/><br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nNot a function<\/p>\n<p>Explanation:<br \/>\nThe input value is 4 is paired with two outputs 25 and 35<\/p>\n<p>Question 6.<br \/>\nThe graph shows the relationship between the weights of 5 packages and the shipping charge for each package. Is the relationship represented by the graph a function? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 6\" width=\"238\" height=\"219\" \/><br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nFunction<\/p>\n<p>Explanation:<br \/>\nEach input is assigned to exactly one output.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 7.<br \/>\nWhat are four different ways of representing functions? How can you tell if a relationship is a function?<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nThe function can be represented by an equation, table, graph, and Venn diagram.<br \/>\nIf a relationship is a function, each input is paired with exactly one output.<\/p>\n<h3><a id=\"\u00b7_Identifying_and_Representing_Functions_\u2013_Page_No._159\"><\/a>Independent Practice &#8211; Identifying and Representing Functions &#8211; Page No. 159<\/h3>\n<p><strong>Determine whether each relationship represented by the ordered pairs is a function. Explain.<\/strong><\/p>\n<p>Question 8.<br \/>\n(2, 2), (3, 1), (5, 7), (8, 0), (9, 1)<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nFunction<\/p>\n<p>Explanation:<br \/>\nEach input value is paired with exactly one output value.<\/p>\n<p>Question 9.<br \/>\n(0, 4), (5, 1), (2, 8), (6, 3), (5, 9)<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nNot a function<\/p>\n<p>Explanation:<br \/>\nThe input value is 5 is paired with two outputs 1 and 9<\/p>\n<p>Question 10.<br \/>\nDraw Conclusions<br \/>\nJoaquin receives $0.40 per pound for 1 to 99 pounds of aluminum cans he recycles. He receives $0.50 per pound if he recycles more than 100 pounds. Is the amount of money Joaquin receives a function of the weight of the cans he recycles? Explain your reasoning.<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nThe amount of money increases with the weight of the cans. No weight will result in the same amount of money earned.<\/p>\n<p>Question 11.<br \/>\nA biologist tracked the growth of a strain of bacteria, as shown in the graph.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 7\" width=\"213\" height=\"221\" \/><br \/>\na. Explain why the relationship represented by the graph is a function.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nThe relationship is a function as each input has been assigned exactly one output. There is only one number of bacteria for each number of hours.<\/p>\n<p>Question 11.<br \/>\nb. What If?<br \/>\nSuppose there was the same number of bacteria for two consecutive hours. Would the graph still represent a function? Explain.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nYes. If the number of bacteria for two consecutive hours is the same, one input will still be paired with one output, hence the relationship is still a function.<\/p>\n<p>Question 12.<br \/>\nMultiple Representations<br \/>\nGive an example of a function in everyday life, and represent it as a graph, a table, and a set of ordered pairs. Describe how you know it is a function.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 8\" width=\"432\" height=\"166\" \/><br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nThe cost of a bouquet of flowers and the number of flowers in the bouquet is a function. The unit cost of flowers = $0.85 and x the number of flowers. Hence, C= 0.85x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-4-300x235.png\" alt=\"Grade 8 Chapter 6 image 4\" width=\"300\" height=\"235\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-4-300x235.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-4.png 615w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-5.png\" alt=\"Grade 8 Chapter 6 image 5\" width=\"243\" height=\"221\" \/><br \/>\n(2, 1.7), (4, 3.4), (6, 5.1), (8, 6.8), (10, 8.5)<br \/>\nEach value of the input is paired with exactly one output.<\/p>\n<h3><a id=\"\u00b7_Identifying_and_Representing_Functions_\u2013_Page_No._160\"><\/a>Identifying and Representing Functions &#8211; Page No. 160<\/h3>\n<p><strong>The graph shows the relationship between the weights of six wedges of cheese and the price of each wedge.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 1: Identifying and Representing Functions img 9\" width=\"196\" height=\"251\" \/><\/p>\n<p>Question 13.<br \/>\nIs the relationship represented by the graph a function? Justify your reasoning. Use the words \u201cinput\u201d and \u201coutput\u201d in your explanation, and connect them to the context represented by the graph.<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nYes, the relationship represented by the graph is a function.<br \/>\nEach input (weight) in the graph is paired with exactly one output(price).<\/p>\n<p>Question 14.<br \/>\nAnalyze Relationships<br \/>\nSuppose the weights and prices of additional wedges of cheese were plotted on the graph. Might that change your answer to question 13? Explain your reasoning.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nNo. As the weight of the cheese will increase, the cost of wedges of cheese will increase as well. Hence, for each input (weight), there would be exactly one output (price).<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 15.<br \/>\nJustify Reasoning<br \/>\nA mapping diagram represents a relationship that contains three different input values and four different output values. Is the relationship a function? Explain your reasoning.<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nNo. Since there are three inputs and four outputs, one of the inputs will have more than one output, hence the relationship cannot be a function.<\/p>\n<p>Question 16.<br \/>\nCommunicate Mathematical Ideas<br \/>\nAn onion farmer is hiring workers to help harvest the onions. He knows that the number of days it will take to harvest the onions is a function of the number of workers he hires. Explain the use of the word \u201cfunction\u201d in this context.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nNumber of days = f(number of workers)<\/p>\n<p>Explanation:<br \/>\nWe know that the more the number of workers will be involved in the harvesting of onion, the lesser days it will take to complete.<br \/>\nThus the number of workers becomes the independent variable and the number of days becomes the dependent variable.<br \/>\nHere the word function is used to describe that the number of days is dependent on the number of workers.<br \/>\nNumber of days = f(number of workers)<\/p>\n<h3><a id=\"\u00b7_Describing_Functions_\u2013_Page_No._164\"><\/a>Guided Practice &#8211; Describing Functions &#8211; Page No. 164<\/h3>\n<p><strong>Plot the ordered pairs from the table. Then graph the function represented by the ordered pairs and tell whether the function is linear or nonlinear.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = 5 \u2212 2x<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 10\" width=\"338\" height=\"445\" \/><br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-6.png\" alt=\"Grade 8 Chapter 6 image 6\" width=\"293\" height=\"155\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-7-222x300.png\" alt=\"Grade 8 Chapter 6 image 7\" width=\"222\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-7-222x300.png 222w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-7.png 406w\" sizes=\"(max-width: 222px) 100vw, 222px\" \/><br \/>\nGraph of a linear function is a straight line<br \/>\nLinear relationship<\/p>\n<p>Explanation:<br \/>\nGiven y = 5 &#8211; 2x<br \/>\ny = 5 &#8211; 2(-1) = 5 + 2 = 7<br \/>\ny = 5 &#8211; 2(1) = 5 &#8211; 2 = 3<br \/>\ny = 5 &#8211; 2(3) = 5 &#8211; 6 = -1<br \/>\ny = 5 &#8211; 2(5) = 5 &#8211; 10 = -5<\/p>\n<p>Question 2.<br \/>\ny = 2 \u2212 x<sup>2<\/sup><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 11\" width=\"345\" height=\"435\" \/><br \/>\n_______________<\/p>\n<p>Answer:<br \/>\ny = 2 \u2212 x<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-7802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-8.png\" alt=\"Grade 8 Chapter 6 image 8\" width=\"287\" height=\"177\" \/><br \/>\nGraph the ordered pairs. Then draw a line through the points to represent the solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-9-244x300.png\" alt=\"Grade 8 Chapter 6 image 9\" width=\"244\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-9-244x300.png 244w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-9.png 343w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><br \/>\nGraph of a linear function is not a straight line<br \/>\nNon-linear relationship<\/p>\n<p>Explanation:<br \/>\ny = 2 \u2212 x<sup>2<br \/>\n<\/sup>y = 2 &#8211; 4 = -2<br \/>\ny = 2 &#8211; 1 = 1<br \/>\ny = 2 &#8211; 0 = 2<br \/>\ny = 2 &#8211; 1 = 1<br \/>\ny = 2 &#8211; 4 = -2<\/p>\n<p><strong>Explain whether each equation is a linear equation.<\/strong><\/p>\n<p>Question 3.<br \/>\ny = x<sup>2<\/sup> \u2013 1<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nThe equation is not in the form of a linear equation, hence is not a linear equation.<\/p>\n<p>Explanation:<br \/>\nCompare the equation with the general linear equation y = mx + b.<br \/>\nThe equation is not in the form of a linear equation, hence is not a linear equation.<\/p>\n<p>Question 4.<br \/>\ny = 1 \u2013 x<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nThe equation is in the form of a linear equation, hence is a linear equation.<\/p>\n<p>Explanation:<br \/>\nCompare the equation with the general linear equation y = mx + b.<br \/>\nThe equation is in the form of a linear equation, hence is a linear equation.<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 5.<br \/>\nExplain how you can use a table of values, an equation, and a graph to determine whether a function represents a proportional relationship.<br \/>\nType below:<br \/>\n_______________<\/p>\n<p>Answer:<br \/>\nFrom a table, determine the ratio y\/x. If it is constant the relationship is proportional.<br \/>\nFrom a graph, note if the graph passes through the origin. The graph of a proportional relationship must pass through the origin (0, 0).<br \/>\nFrom an equation, compare with general linear form of equation, y = mx + b. If b = 0, the relationship is proportional.<\/p>\n<h3><a id=\"\u00b7_Describing_Functions_\u2013_Page_No._165\"><\/a>Independent Practice &#8211; Describing Functions &#8211; Page No. 165<\/h3>\n<p>Question 6.<br \/>\nState whether the relationship between x and y in y = 4x \u2013 5 is proportional or nonproportional. Then graph the function.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 12\" width=\"253\" height=\"258\" \/><br \/>\n_______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-246x300.png\" alt=\"Grade 8 Chapter 6 image 10\" width=\"246\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-246x300.png 246w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10.png 471w\" sizes=\"(max-width: 246px) 100vw, 246px\" \/><\/p>\n<p>Explanation:<br \/>\nFirst, we compare the equation with the general linear equation y = mx + b. y = 4x &#8211; 5 is in the form of y = mx + b, with m = 4 and b = -5. Therefore, the equation is a linear equation. Since b is not equal to 0, the relationship is non-proportional.<br \/>\nThen, we choose several values for the input x. We substitute these values of x in the equation to find the output y.<br \/>\ny = 4x \u2013 5<br \/>\nIf x = 0; y = 4(0) &#8211; 5 = -5; (0, -5)<br \/>\nIf x = 2; y = 4(2) &#8211; 5 = 3; (2, 3)<br \/>\nIf x = 4; y = 4(4) &#8211; 5 = 11; (4, 11)<br \/>\nIf x = 6; y = 4(6) &#8211; 5 = 19; (6, 19)<br \/>\nWe graph the ordered pairs and we draw a line through the points to represent the solutions of the function.<\/p>\n<p>Question 7.<br \/>\nThe Fortaleza telescope in Brazil is a radio telescope. Its shape can be approximated with the equation y = 0.013x<sup>2<\/sup>. Is the relationship between x and y linear? Is it proportional? Explain.<br \/>\n____________<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nCompare the equation with the general linear equation y = mx + b.<br \/>\nThe equation is not in the form of a linear equation, hence it is not a linear equation. Since x is squared, it is not proportional.<\/p>\n<p>Question 8.<br \/>\nKiley spent $20 on rides and snacks at the state fair. If x is the amount she spent on rides, and y is the amount she spent on snacks, the total amount she spent can be represented by the equation x + y = 20. Is the relationship between x and y linear? Is it proportional? Explain.<br \/>\n____________<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nx + y = 20<br \/>\nRewriting the equation<br \/>\ny = 20 &#8211; x<br \/>\nCompare the equation with the general linear equation y = mx + b.<br \/>\nIt is linear<br \/>\nSince b is not equal to 0, the relationship is not proportional.<\/p>\n<p>Question 9.<br \/>\nRepresent Real-World Problems<br \/>\nThe drill team is buying new uniforms. The table shows y, the total cost in dollars, and x, the number of uniforms purchased.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 13\" width=\"590\" height=\"222\" \/><br \/>\na. Use the data to draw a graph. Is the relationship between x and y linear? Explain.<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-1-300x177.png\" alt=\"Grade 8 Chapter 6 image 10\" width=\"300\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-1-300x177.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-1.png 717w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe graph of a linear relationship is a straight line.<br \/>\nx and y are linear.<\/p>\n<p>Question 9.<br \/>\nb. Use your graph to predict the cost of purchasing 12 uniforms.<br \/>\n$ ________<\/p>\n<p>Answer:<br \/>\n$720<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-2-300x179.png\" alt=\"Grade 8 Chapter 6 image 10\" width=\"300\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-2-300x179.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-10-2.png 711w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe cost of 12 uniforms is $720<\/p>\n<p>Question 10.<br \/>\nMarta, a whale calf in an aquarium, is fed a special milk formula. Her handler uses a graph to track the number of gallons of formula y the calf drinks in x hours. Is the relationship between x and y linear? Is it proportional? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 14\" width=\"221\" height=\"228\" \/><br \/>\n____________<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nThe relationship is linear<br \/>\nThe relationship is proportional<\/p>\n<p>Explanation:<br \/>\nAs the data lies on a straight line, the relationship is linear<br \/>\nAs the graph passes through the origin, the relationship is proportional<\/p>\n<h3><a id=\"\u00b7_Describing_Functions_\u2013_Page_No._166\"><\/a>Describing Functions &#8211; Page No. 166<\/h3>\n<p>Question 11.<br \/>\nCritique Reasoning<br \/>\nA student claims that the equation y = 7 is not a linear equation because it does not have the form y=mx + b. Do you agree or disagree? Why?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 2: Describing Functions img 15\" width=\"289\" height=\"253\" \/><br \/>\n____________<\/p>\n<p>Answer:<br \/>\nDisagree; The equation can be written in the form y = mx + b Where m is 0. The graph of the solutions is a horizontal line.<\/p>\n<p>Question 12.<br \/>\nMake a Prediction<br \/>\nLet x represent the number of hours you read a book and y represent the total number of pages you have read. You have already read 70 pages and can read 30 pages per hour. Write an equation relating x hours and y pages you read. Then predict the total number of pages you will have read after another 3 hours.<br \/>\n_______ pages<\/p>\n<p>Answer:<br \/>\n160 pages<\/p>\n<p>Explanation:<br \/>\nLet x represent the number of hours you read a book and y represents the total number of pages you have read. You have already read 70 pages and can read 30 pages per hour.<br \/>\nm = 30; b = 70 pages<br \/>\ny = 30x + 70<br \/>\nx = 3 hrs<br \/>\ny = 30(3) + 70 = 160<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 13.<br \/>\nDraw Conclusions<br \/>\nRebecca draws a graph of a real-world relationship that turns out to be a set of unconnected points. Can the relationship be linear? Can it be proportional? Explain your reasoning.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe relationship is linear if all the points lie on the same line. If the relationship is linear and passes through the origin, it is proportional.<\/p>\n<p>Question 14.<br \/>\nCommunicate Mathematical Ideas<br \/>\nWrite a real-world problem involving a proportional relationship. Explain how you know the relationship is proportional.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe amount of money earned at a car wash is a proportional relationship. When there are 0 cars washed, $0 are earned. The amount of money earned increases by the unit cost of a car wash.<\/p>\n<p>Question 15.<br \/>\nJustify Reasoning<br \/>\nShow that the equation y + 3 = 3(2x + 1) is linear and that it represents a proportional relationship between x and y.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny + 3 = 3(2x + 1)<br \/>\ny +3 = 6x + 3<br \/>\ny = 6x<br \/>\nAs b = 0, it is a Proportional Relationship.<\/p>\n<h3><a id=\"\u00b7_Comparing_Functions_\u2013_Page_No._170\"><\/a>Guided Practice &#8211; Comparing Functions &#8211; Page No. 170<\/h3>\n<p><strong>Doctors have two methods of calculating maximum heart rate. With the first method, maximum heart rate, y, in beats per minute is y = 220 \u2212 x, where x is the person\u2019s age. Maximum heart rate with the second method is shown in the table.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 16\" width=\"530\" height=\"61\" \/><\/p>\n<p>Question 1.<br \/>\nWhich method gives the greater maximum heart rate for a 70-year-old?<br \/>\n____________ method<\/p>\n<p>Answer:<br \/>\nSecond<\/p>\n<p>Explanation:<br \/>\ny = 220 &#8211; x<br \/>\ny = 220 &#8211; 70 = 150<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (20, 194) and (x2, y2) = (30, 187)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (187 \u2013 194)\/(30 \u2013 20) = -7\/10 = -0.7<br \/>\n197 = -0.7(20) + b<br \/>\ny-intercept b = 208<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = -0.7 and b = 208.<br \/>\ny = -0.7x +208<br \/>\nx = 70yrs<br \/>\ny = -0.7(70) + 208 = 159<br \/>\n150 &lt; 159<br \/>\nSecond method gives the greater maximum heart rate for a 70 year ols.<\/p>\n<p>Question 2.<br \/>\nAre heart rate and age proportional or nonproportional for each method?<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nFor method 1, the relationship is non-propotional.<br \/>\nFor method 2, the relationship is non-propotional.<\/p>\n<p>Explanation:<br \/>\nCompare the equation with the general linear equation y = mx + b.<br \/>\nIt is linear<br \/>\nSince b is not equal to 0, the relationship is not proportional.<\/p>\n<p><strong>Aisha runs a tutoring business. With Plan 1, students may choose to pay $15 per hour. With Plan 2, they may follow the plan shown on the graph.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 17\" width=\"208\" height=\"186\" \/><\/p>\n<p>Question 3.<br \/>\nDescribe the plan shown on the graph.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nChoose two points on the graph to find the slope.<br \/>\nFind the slope<br \/>\nm = (y2 -y1)\/(x2 \u2013 x1)<br \/>\nm = (60 &#8211; 40)\/(4 &#8211; 0) = 20\/4 = 5<br \/>\nRead the y-intercept from the graph: b = 40<br \/>\nUse your slope and y-intercept values to write an equation in slope-intercept<br \/>\nform.<br \/>\ny = 5x + 40<br \/>\nPlan 2 has an intial cost of $40 and a rate of $5 per hour.<\/p>\n<p>Question 4.<br \/>\nSketch a graph showing the $15 per hour option.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-11-244x300.png\" alt=\"Grade 8 Chapter 6 image 11\" width=\"244\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-11-244x300.png 244w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-11.png 457w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/p>\n<p>Question 5.<br \/>\nWhat does the intersection of the two graphs mean?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe intersection of the two graphs represents the number of hours for which both plans will cost the same,<\/p>\n<p>Question 6.<br \/>\nWhich plan is cheaper for 10 hours of tutoring?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPlan 1<br \/>\ny = 15x<br \/>\nx = 10 hrs<br \/>\ny = 15(10) = $150<br \/>\nPlan 2<br \/>\ny = 5x + 40<br \/>\ny = 5(10) + 40 = $90<br \/>\n$150 &gt; $90<br \/>\nPlane 2 is cheaper<\/p>\n<p>Question 7.<br \/>\nAre cost and time proportional or nonproportional for each plan?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nComparing with the general linear form of equation y = mx + b. Since b = 0, the relationship is proportional<br \/>\nThe cost and time are proportional for Plan 1<br \/>\nComparing with the general linear form of equation y = mx + b. Since b is not equal to 0, the relationship is proportional<br \/>\nThe cost and time are not proportional for Plan 2<\/p>\n<p><strong>Essential Question Check-In<\/strong><\/p>\n<p>Question 8.<br \/>\nWhen using tables, graphs, and equations to compare functions, why do you find the equations for tables and graphs?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe tables and graphs represent a part of the solution of the function. By writing the equation, any value can be a substitute to evaluate the function and compared it with the equations.<\/p>\n<h3><a id=\"\u00b7_Comparing_Functions_\u2013_Page_No._171\"><\/a>Independent Practice &#8211; Comparing Functions &#8211; Page No. 171<\/h3>\n<p><strong>The table and graph show the miles driven and gas used for two scooters.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 18\" width=\"651\" height=\"219\" \/><\/p>\n<p>Question 9.<br \/>\nWhich scooter uses fewer gallons of gas when 1350 miles are driven?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nScooter B uses fewer gallons of gas when 1350 miles are driven<\/p>\n<p>Explanation:<br \/>\nThe equation for Scooter A Slope m = m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (150, 2) and (x2, y2) = (300, 4)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (4 \u2013 2)\/(300 \u2013 150) = 2\/150 = 1\/75<br \/>\n2 = 1\/75(150) + b<br \/>\ny-intercept b = 0<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1\/75 and b = 0.<br \/>\ny = 1\/75x<br \/>\nx = 1350 miles<br \/>\ny = 1\/75(1,350)<br \/>\ny = 18gal<br \/>\nThe equation for Scooter B Slope m = m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, 0) and (x2, y2) = (90, 1)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (1 \u2013 0)\/(90 \u2013 0) = 1\/90<br \/>\n2 = 1\/90(90) + b<br \/>\ny-intercept b = 0<br \/>\nSubstituting the value of the slope m and y-intercept in the slope-intercept form. y = mx + b where, m = 1\/90 and b = 0.<br \/>\ny = 1\/90x<br \/>\nx = 1350 miles<br \/>\ny = 1\/90(1,350)<br \/>\ny = 15gal<br \/>\nCompare the gallons of gas to drive 1,350 miles<br \/>\n18 &gt; 15<br \/>\nScooter B uses fewer gallons of gas when 1,350 miles are driven.<\/p>\n<p>Question 10.<br \/>\nAre gas used and miles proportional or nonproportional for each scooter?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe gas used and miles are proportional to both scooters.<\/p>\n<p>Explanation:<br \/>\nCompare with general linear form of an equation, y = mx + b. If b = 0, the relationship is proportional.<br \/>\nThe gas used and miles are proportional to both scooters.<\/p>\n<p><strong>A cell phone company offers two texting plans to its customers. The monthly cost, y dollars, of one plan is y = 0.10x + 5, where x is the number of texts. The cost of the other plan is shown in the table.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 19\" width=\"513\" height=\"88\" \/><\/p>\n<p>Question 11.<br \/>\nWhich plan is cheaper for under 200 texts?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPlane 1 is cheaper<\/p>\n<p>Explanation:<br \/>\nPlan 1<br \/>\ny = 0.10x + 5<br \/>\nSubsitute x = 199<br \/>\ny = 0.10(199) + 5 = $24.90<br \/>\nFind the slope using two points from the graph by m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (100, 20), (x2, y2) =(200, 25)<br \/>\nSubstitute the value of m and (x1, y1) = (100, 20), (x2, y2) =(200, 25)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (25 &#8211; 20)\/(200 \u2013 100) = 5\/100 = 0.05<br \/>\n20 = 0.05(100) + b<br \/>\ny-intercept b = 15<br \/>\nSubstituting the value of slope (m) and (x, y) in the slope intercept form to find y intercept (b):<br \/>\ny = 0.05x + 15<br \/>\nx = 199<br \/>\ny = 0.05(199) + 15 = $24.95<br \/>\nCompare the cost for two plans for text &lt; 200<br \/>\n$24.90 &lt; $24.95<br \/>\nPlane 1 is cheaper<\/p>\n<p>Question 12.<br \/>\nThe graph of the first plan does not pass through the origin. What does this indicate?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPlan 1<br \/>\ny = 0.10x + 5<br \/>\nThe graph that does not pass through the origin indicates that there is a base price of $5 for the plan.<\/p>\n<p>Question 13.<br \/>\nBrianna wants to buy a digital camera for a photography class. One store offers the camera for $50 down and a payment plan of $20 per month. The payment plan for a second store is described by y = 15x + 80, where y is the total cost in dollars and x is the number of months. Which camera is cheaper when the camera is paid off in 12 months? Explain.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nFor first store, the slope interecept form y = mx + b where m = 20 dollars per month and b = 50 dollar.<br \/>\ny = 20x + 50<br \/>\nx = 12 months<br \/>\ny = 20(12) + 50 = $290<br \/>\nSecond store<br \/>\ny = 15x + 80<br \/>\nx = 12 months<br \/>\ny = 15(12) + 80 = $260<br \/>\nCompare the cost of camera if it paid off in 12 months $290 &gt; $260<br \/>\nCamera is cheaper at second store<\/p>\n<h3><a id=\"\u00b7_Comparing_Functions_\u2013_Page_No._172\"><\/a>Comparing Functions &#8211; Page No. 172<\/h3>\n<p>Question 14.<br \/>\nThe French club and soccer team are washing cars to earn money. The amount earned, y dollars, for washing x cars is a linear function. Which group makes the most money per car? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 3: Comparing Functions img 20\" width=\"678\" height=\"208\" \/><br \/>\n______________<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (2, 10) and (x2, y2) = (4, 20)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (20 \u2013 10)\/(4 \u2013 2) = 10\/2 = 5<br \/>\nFrench Club makes $5 per car.<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (0, 0) and (x2, y2) = (2, 16)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (16 \u2013 0)\/(2 \u2013 0) = 16\/2 = 8<br \/>\nSoccer Club makes $8 per car.<br \/>\nCompare the money earned for washing one car $5 &lt; $8<br \/>\nSoccer club makes the most money per car<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><\/p>\n<p>Question 15.<br \/>\nDraw Conclusions<br \/>\nGym A charges $60 a month plus $5 per visit. The monthly cost at Gym B is represented by y = 5x + 40, where x is the number of visits per month. What conclusion can you draw about the monthly costs of the gyms?<br \/>\n__________ is more expensive<\/p>\n<p>Answer:<br \/>\nGym A is more expensive<\/p>\n<p>Explanation:<br \/>\nSince the rate per visit is the same, the monthly cost of Gyn A is always more than Gym B.<\/p>\n<p>Question 16.<br \/>\nJustify Reasoning<br \/>\nWhy will the value of y for the function y = 5x + 1 always be greater than that for the function y = 4x + 2 when x &gt; 1?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny1 = 5x + 1 and y2 = 4x + 2 Subtracting y2 from y1<br \/>\ny1 &#8211; y2 = 5x + 1 &#8211; (4x + 2)<br \/>\ny1 &#8211; y2 = x -1<br \/>\nFor x&gt;= 1 we get x &#8211; 1 &gt;= 0<br \/>\nSo y1 &#8211; y2 &gt;= 0 or y1 &gt;= y2<\/p>\n<p>Question 17.<br \/>\nAnalyze Relationships<br \/>\nThe equations of two functions are y = \u221221x + 9 and y = \u221224x + 8. Which function is changing more quickly? Explain.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = -21x + 9<br \/>\ny = -24x + 8<br \/>\ny = -24x + 8 is changing more quickly as the absolute value of -24 is greater than the absolute value of -21.<\/p>\n<h3><a id=\"Analyzing_Graphs_\u2013_Page_No._176\"><\/a>Guided Practice &#8211; Analyzing Graphs &#8211; Page No. 176<\/h3>\n<p><strong>In a lab environment, colonies of bacteria follow a predictable pattern of growth. The graph shows this growth over time.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 21\" width=\"282\" height=\"286\" \/><\/p>\n<p>Question 1.<br \/>\nWhat is happening to the population during Phase 2?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nFor Phase 2, the graph is increasing quickly. This shows a period of rapid growth.<\/p>\n<p>Question 2.<br \/>\nWhat is happening to the population during Phase 4?<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nIn Phase 4, the graph is decreasing, hence the number of bacterias is decreasing.<\/p>\n<p><strong>The graphs give the speeds of three people who are riding snowmobiles. Tell which graph corresponds to each situation.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 22\" width=\"652\" height=\"209\" \/><\/p>\n<p>Question 3.<br \/>\nChip begins his ride slowly but then stops to talk with some friends. After a few minutes, he continues his ride, gradually increasing his speed.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nGraph 2<\/p>\n<p>Explanation:<br \/>\nThe slope of the graph is increasing, then it becomes constant and starts increasing again.<br \/>\nGraph 2<\/p>\n<p>Question 4.<br \/>\nLinda steadily increases her speed through most of her ride. Then she slows down as she nears some trees.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nGraph 3<\/p>\n<p>Explanation:<br \/>\nThe slope of the graph is increasing and then decreasing.<br \/>\nGraph 3<\/p>\n<p>Question 5.<br \/>\nPaulo stood at the top of a diving board. He walked to the end of the board, and then dove forward into the water. He plunged down below the surface, then swam straight forward while underwater. Finally, he swam forward and upward to the surface of the water. Draw a graph to represent Paulo\u2019s elevation at different distances from the edge of the pool.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 23\" width=\"188\" height=\"211\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-12-300x178.png\" alt=\"Grade 8 Chapter 6 image 12\" width=\"300\" height=\"178\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-12-300x178.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-12.png 717w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h3><a id=\"\u00b7_Analyzing_Graphs_\u2013_Page_No._177\"><\/a>Independent Practice &#8211; Analyzing Graphs &#8211; Page No. 177<\/h3>\n<p><strong>Tell which graph corresponds to each situation below.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 24\" width=\"707\" height=\"275\" \/><\/p>\n<p>Question 6.<br \/>\nArnold started from home and walked to a friend\u2019s house. He stayed with his friend for a while and then walked to another friend\u2019s house farther from home.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nGraph 3<\/p>\n<p>Explanation:<br \/>\nThe graph increases (as Arnold walks from home to friend&#8217;s house), then becomes constant (when he stayed with his friend) and then increases again (when he walk to another friend&#8217;s house farther away).<br \/>\nGraph 3<\/p>\n<p>Question 7.<br \/>\nFrancisco started from home and walked to the store. After shopping, he walked back home.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nGraph 1<\/p>\n<p>Explanation:<br \/>\nThe graph increases (as Francisco walked from home to store), becomes constant (when he shops), and then decreases (as he walked back home)<br \/>\nGraph 1<\/p>\n<p>Question 8.<br \/>\nCelia walks to the library at a steady pace without stopping.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nGraph 2<\/p>\n<p>Explanation:<br \/>\nThe graph increases at a constant rate (as Celia walks to library without any stops)<br \/>\nGraph 2<\/p>\n<p><strong>Regina rented a motor scooter. The graph shows how far away she is from the rental site after each half hour of riding.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 25\" width=\"224\" height=\"296\" \/><\/p>\n<p>Question 9.<br \/>\nRepresent Real-World Problems<br \/>\nUse the graph to describe Regina\u2019s trip. You can start the description like this: \u201cRegina left the rental shop and rode for an hour\u2026\u201d<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nRegina left the rental shop and rode for an hour. She rested for half an hour and then started back. After half an hour, she changed her mind and rode for another half an hour. She rest for half an hour. Then she started back and ranched the rental site in 2 hours.<\/p>\n<p>Question 10.<br \/>\nAnalyze Relationships<br \/>\nDetermine during which half hour Regina covered the greatest distance.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nRegina covered the greatest distance between 0.5 to 1hr of the journey. She covered 12 miles.<\/p>\n<h3><a id=\"\u00b7_Analyzing_Graphs_\u2013_Page_No._178\"><\/a>Analyzing Graphs &#8211; Page No. 178<\/h3>\n<p><strong>The data in the table shows the speed of a ride at an amusement park at different times one afternoon.<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 26\" width=\"640\" height=\"253\" \/><\/p>\n<p>Question 11.<br \/>\nSketch a graph that shows the speed of the ride over time.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-13-300x180.png\" alt=\"Grade 8 Chapter 6 image 13\" width=\"300\" height=\"180\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-13-300x180.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-13.png 712w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 12.<br \/>\nBetween which times is the ride\u2019s speed increasing the fastest?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe speed is increasing the fastest during the 3: 21 and 3: 22<\/p>\n<p>Question 13.<br \/>\nBetween which times is the ride\u2019s speed decreasing the fastest?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe speed is decreasing the fastest during the 3: 23 and 3: 24<\/p>\n<p><strong>H.O.T.<\/strong><\/p>\n<p><strong>Focus on Higher Order Thinking<\/strong><br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-27.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 27\" width=\"264\" height=\"193\" \/><\/p>\n<p>Question 14.<br \/>\nJustify Reasoning<br \/>\nWhat is happening to the fox population before time t? Explain your reasoning.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-28.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 28\" width=\"264\" height=\"193\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe population decreases and then increases before time t<\/p>\n<p>Question 15.<br \/>\nWhat If?<br \/>\nSuppose at time t, a conservation organization moves a large group of foxes to the island. Sketch a graph to show how this action might affect the population on the island after time t.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-29.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Lesson 4: Analyzing Graphs img 29\" width=\"242\" height=\"173\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-7819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-14-300x250.jpg\" alt=\"Grade 8 Chapter 6 image 14\" width=\"300\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-14-300x250.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Grade-8-Chapter-6-image-14.jpg 402w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nPopulation is decreasing at first, then it is increasing rapidly.<\/p>\n<p>Question 16.<br \/>\nMake a Prediction<br \/>\nAt some point after time t, a forest fire destroys part of the woodland area on the island. Describe how your graph from problem 15 might change.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe population would dramatically decrease if there was a fire due to lack of food supply and good land.<\/p>\n<h3><a id=\"\u00b7_Model_Quiz_\u2013_Page_No._179\"><\/a>6.1 Identifying and Representing Functions &#8211; Model Quiz &#8211; Page No. 179<\/h3>\n<p><strong>Determine whether each relationship is a function.<\/strong><\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-30.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Model Quiz img 30\" width=\"159\" height=\"128\" \/><br \/>\n__________<\/p>\n<p>Answer:<br \/>\nNot a function<\/p>\n<p>Explanation:<br \/>\nA relationship is a function when each input is paired with exactly one output. The input 5 has more than one output.<br \/>\nNot a function<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-31.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Model Quiz img 31\" width=\"174\" height=\"132\" \/><br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFunction<\/p>\n<p>Explanation:<br \/>\nA relationship is a function when each input is paired with exactly one output.<br \/>\nEach input is paired with only one output.<br \/>\nFunction<\/p>\n<p>Question 3.<br \/>\n(2, 5), (7, 2), (\u22123, 4), (2, 9), (1, 1)<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nNot a function<\/p>\n<p>Explanation:<br \/>\nA relationship is a function when each input is paired with exactly one output. Input 2 has more than one output.<br \/>\nNot a function<\/p>\n<p><strong>6.2 Describing Functions<\/strong><\/p>\n<p><strong>Determine whether each situation is linear or nonlinear, and proportional or nonproportional.<\/strong><\/p>\n<p>Question 4.<br \/>\nJoanna is paid $14 per hour.<br \/>\n__________<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLinear<br \/>\nProportional<\/p>\n<p>Explanation:<br \/>\nWriting the situation as an equation, where x is the number of hours.<br \/>\ny = 14x<br \/>\nCompare with general linear equation y = mx + b<br \/>\nLinear<br \/>\nSince b = 0, the relationship is proportional.<br \/>\nProportional<\/p>\n<p>Question 5.<br \/>\nAlberto started out bench pressing 50 pounds. He then added 5 pounds every week.<br \/>\n__________<br \/>\n__________<\/p>\n<p>Answer:<br \/>\nLinear<br \/>\nNon-proportional<\/p>\n<p>Explanation:<br \/>\nWriting the situation as an equation, where x is the number of hours.<br \/>\ny = 5x + 50<br \/>\nCompare with general linear equation y = mx + b<br \/>\nLinear<br \/>\nSince b is not equal to 0, the relationship is non-proportional.<br \/>\nNon-proportional<\/p>\n<p><strong>6.3 Comparing Functions<\/strong><\/p>\n<p>Question 6.<br \/>\nWhich function is changing more quickly? Explain.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-32.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Model Quiz img 32\" width=\"367\" height=\"212\" \/><br \/>\n__________<\/p>\n<p>Answer:<br \/>\nFunction 2 is changing more quickly.<\/p>\n<p>Explanation:<br \/>\nFind the rate of change for function 1<br \/>\nRate of Change = (20 &#8211; 0)\/(0 &#8211; 5) = -4<br \/>\nFind the rate of change for function 1<br \/>\nRate of Change = (6.5 &#8211; 11)\/(3 &#8211; 2) = -4.5<br \/>\nAlthogh -4.5 &lt; -4, the absolute value of -4.5 s greater than -4.<br \/>\nFunction 2 is changing more quickly.<\/p>\n<p><strong>6.4 Analyzing Graphs<\/strong><\/p>\n<p>Question 7.<br \/>\nDescribe a graph that shows Sam running at a constant rate.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe graph would be a straight line<\/p>\n<p>Explanation:<br \/>\nSince Sam is running at a constant rate, distance covered per unit of time remains the same and the relationship is linear and proportional.<br \/>\nThe graph would be a straight line<\/p>\n<p><strong>Essential Question<\/strong><\/p>\n<p>Question 8.<br \/>\nHow can you use functions to solve real-world problems?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nIf in the equation the power of x is 1 then it is linear otherwise nonlinear.<br \/>\nIn a graph, if the points form a line it is linear if they form a curve it is a nonlinear function.<\/p>\n<h3><a id=\"\u00b7_Mixed_Review_\u2013_Page_No._180\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 180<\/h3>\n<p>Question 1.<br \/>\nWhich table shows a proportional function?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-33.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 33\" width=\"226\" height=\"289\" \/><br \/>\nOptions:<br \/>\na. A<br \/>\nb. B<br \/>\nc. C<br \/>\nd. D<\/p>\n<p>Answer:<br \/>\nc. C<\/p>\n<p>Explanation:<br \/>\nIt contains the ordered pair of the origin (0, 0)<br \/>\nOption C represents a proportional relationship.<\/p>\n<p>Question 2.<br \/>\nWhat is the slope and y-intercept of the function shown in the table?<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-34.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 34\" width=\"182\" height=\"69\" \/><br \/>\nOptions:<br \/>\na. m = -2; b = -4<br \/>\nb. m = -2; b = 4<br \/>\nc. m = 2; b = 4<br \/>\nd. m = 4; b = 2<\/p>\n<p>Answer:<br \/>\nc. m = 2; b = 4<\/p>\n<p>Explanation:<br \/>\nFind the slope using two points from the grapgh by<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (1, 6) and (x2, y2) = (4, 12)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (12 \u2013 6)\/(4 \u2013 1) = 6\/3 = 2<br \/>\nSubstituting the value of the slope m and (x, y) to find the slope-intercept form.<br \/>\n12 = 4(2) + b<br \/>\ny-intercept b = 4<\/p>\n<p>Question 3.<br \/>\nThe table below shows some input and output values of a function.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-35.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 35\" width=\"289\" height=\"71\" \/><br \/>\nWhat is the missing output value?<br \/>\nOptions:<br \/>\na. 20<br \/>\nb. 21<br \/>\nc. 22<br \/>\nd. 23<\/p>\n<p>Answer:<br \/>\nb. 21<\/p>\n<p>Explanation:<br \/>\nFind the rate of change = (17.5 &#8211; 14)\/(5 &#8211; 4) = 3.5<br \/>\nSince the missing output is corresponding to x = 6 and 3.5 to 17.5 (for x = 5)<br \/>\nOutput = 17.5 + 3.5 = 21<\/p>\n<p>Question 4.<br \/>\nTom walked to school at a steady pace, met his sister, and they walked home at a steady pace. Describe this graph.<br \/>\nOptions:<br \/>\na. V-shaped<br \/>\nb. upside down V-shaped<br \/>\nc. Straight line sloping up<br \/>\nd. Straight line sloping down<\/p>\n<p>Answer:<br \/>\nb. upside-down V-shaped<\/p>\n<p>Explanation:<br \/>\nThe graph would increase at a constant rate and would decrease at a constant rate.<br \/>\nThe graph would be the upside-down V-shaped<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 5.<br \/>\nLinear functions can be used to find the price of a building based on its floor area.Below are two of these functions.<br \/>\ny = 40x + 15,000<br \/>\n<img loading=\"lazy\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-6-Functions-img-36.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 6 Functions Mixed Review img 36\" width=\"297\" height=\"69\" \/><br \/>\na. Find and compare the slopes.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nCompare the slopes<br \/>\nThe slope for the first function is less than the slope of the second function.<br \/>\ny = 40x + 15000<br \/>\nCompare with slope intercept form y = mx + b where m is the slope m = 40<br \/>\nSecond function find the slope using given points by Slope m = (y2 -y1)\/(x2 \u2013 x1) where (x1, y1) = (7, 3) and (x2, y2) = (6, 4)<br \/>\nSlope m = (y2 -y1)\/(x2 \u2013 x1) = (56000 \u2013 32000)\/(700 \u2013 400) = 24000\/300 = 80<br \/>\nm = 80<\/p>\n<p>Question 5.<br \/>\nb. Find and compare the y-intercepts.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\ny = 40x + 15,000<br \/>\nCompare with slope-intercept form y = mx + b where m is the slope b = 15000<br \/>\nThe second function find the slope using given points by Slope m and (x, y) in the slope-intercept form to fins y-intercept b<br \/>\ny = mx + b where (x, y) = (700, 56000) and m = 80<br \/>\n56000 = 80(700) + b<br \/>\nb = 0<br \/>\nCompare y intercepts<br \/>\nThe y-intercept of the first function is greater than the y-intercept of the second function<\/p>\n<p>Question 5.<br \/>\nc. Describe each function as proportional or nonproportional.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nComparable to slope interecept form y = mx + b<br \/>\nFirst function: y = 40x + 15000<br \/>\nSecond function: y = 80x<br \/>\nSince b is not equal to 0<br \/>\nFirst function is non-proportional<br \/>\nSince b = 0<br \/>\nThe second function is proportional.<\/p>\n<h3>Conclusion:<\/h3>\n<p>we wish the detailed prevailed in HMH Go Math 8th Grade Chapter 6 Functions are helpful for you to score the best in the exams. Download our Go Math Grade 8 Solution Key Chapter 6 Functions PDF for free of cost. Keep in touch with us to get the fastest updates about the Go Math Grade 8 Chapter 6 Functions Answer Key. For any queries, you can post your comments in the below comment section.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The solutions of Go Math Grade 8 Answer Key Chapter 6 Functions are provided in the pdf format here. HMH Go Math Grade 8 Answer Key Chapter 6 Functions are presented by the professional math experts in an easy manner and with brief explanations. You can find different ways of solving the problems on this &#8230; <a title=\"Go Math Grade 8 Answer Key Chapter 6 Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-6-functions\/\" aria-label=\"More on Go Math Grade 8 Answer Key Chapter 6 Functions\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":8779,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/go-math-grade-8-chapter-6-functions-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6517"}],"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\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=6517"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6517\/revisions"}],"predecessor-version":[{"id":92799,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6517\/revisions\/92799"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8779"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=6517"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=6517"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=6517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}