Functions or Mapping Worksheet with Solutions<\/h2>\n
1. Which of the following represents a mapping? (a) Given that {(5, 3); (6, 4); (8, 6); (10, 8)} Therefore, (a), (b), (d), (e) represents a mapping.<\/p>\n<\/details>\n 2. Which of the following arrow diagrams represents a mapping? (a) Different elements of P can have the same image in Q. Adjoining figure represents a mapping.<\/p>\n (b) Every element of P must have an image in Q. Adjoining figure does not represent a mapping since the element z in set P is not associated with any element of set Q. (c) Every element of P must have an image in Q. Adjoining figure does not represent a mapping since the element y in set P is not associated with any element of set Q.<\/p>\n (d) No element of P must have more than one image. The adjoining figure does not represent a mapping since element x in set P is associated with two elements m, o of set Q.<\/p>\n Therefore, (a) represents a mapping.<\/p>\n<\/details>\n 3. A function f is defined by f(x) = 3x – 5. Write the values of Given that a function f is defined by f(x) = 3x – 5. Therefore, the answer is f(0) = -5<\/p>\n (b) f(-3) Therefore, the answer is f(-3) = -14<\/p>\n (c) f(4) Therefore, the answer is f(4) = 7<\/p>\n (d) f(-2) Therefore, f(0) = -5; f(-3) = -14; f(4) = 7; f(-2) = -11<\/p>\n<\/details>\n 4. Find the range of each of the following functions. (a) Given that f(x) = 7 – x, x \u2208 N, x > 0 Hence, Range = (-\u221e, 7)<\/p>\n (b) Given that f(x) = x\u00b2 + 4, x \u2208 R Hence, Range of f(x) = (4, \u221e)<\/p>\n<\/details>\n 5. Let M = {2, 4, 8, 7} and N = {5, 9, 17, 18, 19} Given that M = {2, 4, 7, 8} and N = {5, 9, 17, 18, 19} 6. Let A = {2, 3, 6} B = {3, 4, 5, 6, 8, 12} Given that A = {2, 3, 6} B = {3, 4, 5, 6, 8, 12} 7. Let A = {4, 9, 12} and B = {2, 3, 4} Given that A = {4, 9, 12} and B = {2, 3, 4} Therefore, R = {(4, 2), (9, 3)} is not a mapping from A to B.<\/p>\n (b) R = {(4, 2); (4, 4); (9, 3); (12, 2); (12, 4)} from A to B Therefore, R = {(4, 2); (4, 4); (9, 3); (12, 2); (12, 4)} from A to B is not a mapping from A to B.<\/p>\n<\/details>\n 8. Let A = {3, 4, 5} and B = {12, 17, 22} Given that A = {3, 4, 5} and B = {12, 17, 22} Therefore, f is a mapping from A to B.<\/p>\n (b) Domain = Set of all first elements in a relation = {3, 4, 5} (c) The mapping in the roster form r = {(3, 12); (4, 17); (5, 22)}<\/p>\n (d) Get better practice by referring to the Worksheet on Functions or Mapping. Students who are interested in learning the complete concept of Functions or Mapping can learn it from Functions Mapping Worksheets. These Worksheets help you to have better practice for exams. We have included different problems along with solutions and explanations for your better … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":87272,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/87246"}],"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=87246"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/87246\/revisions"}],"predecessor-version":[{"id":91356,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/87246\/revisions\/91356"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/87272"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=87246"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=87246"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=87246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n(a) {(5, 3); (6, 4); (8, 6); (10, 8)}
\n(b) {(3, 9); (4, 13); (5, 17)}
\n(c) {(4, 8); (4, 12); (5, 10); (6, 12)}
\n(d) {(2, 3); (3, 4); (4, 5); (5, 6)}
\n(e) {(3, 2); (4, 2); (6, 2); (8, 2)}
\n(f) {(2, 4); (2, 6); (3, 6)}<\/p>\nSolution:<\/summary>\n
\nLet the two sets are P and Q.
\nThe required diagram is
\n![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping.jpg\")
\nDifferent elements of P can have the same image in Q. Adjoining figure represents a mapping.
\n(b) Given that {(3, 9); (4, 13); (5, 17)}
\nLet the two sets are P and Q.
\nThe required diagram is
\n![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping-Question.jpg\")
\nDifferent elements of P can have the same image in Q. Adjoining figure represents a mapping.
\n(c) Given that {(4, 8); (4, 12); (5, 10); (6, 12)}
\nLet the two sets are P and Q.
\nThe required diagram is
\n![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping-Questions.jpg\")
\nNo element of P must have more than one image. The adjoining figure does not represent a mapping since element 4 in set P is associated with two elements 8, 12 of set Q.
\n(d) Given that {(2, 3); (3, 4); (4, 5); (5, 6)}
\nLet the two sets are P and Q.
\nThe required diagram is
\n![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping-Question-and-answer.jpg\")
\nDifferent elements of P can have the same image in Q. Adjoining figure represents a mapping.
\n(e) Given that {(3, 2); (4, 2); (6, 2); (8, 2)}
\nLet the two sets are P and Q.
\nThe required diagram is
\n![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping-Question-and-answers.jpg\")
\nDifferent elements of P can have the same image in Q. Adjoining figure represents a mapping.
\n(f) Given that {(2, 4); (2, 6); (3, 6)}
\nLet the two sets are P and Q.
\nThe required diagram is
\n![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping-Questions-and-answers.jpg\")
\nNo element of P must have more than one image. The adjoining figure does not represent a mapping since element 2 in set P is associated with two elements 4, 6 of set Q.<\/p>\n
\n
\n(a) ![\"Worksheet](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Worksheet-on-Functions-or-Mapping-problems.jpg\")
\n(b) ![\"Functions](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Functions-or-Mapping-Worksheet.jpg\")
\n(c) ![\"Functions](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Functions-or-Mapping-Worksheets.jpg\")
\n(d) ![\"Functions](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Functions-or-Mapping-Worksheet-problems.jpg\")
<\/p>\nSolution:<\/summary>\n
\nNo element of P must have more than one image. The adjoining figure does not represent a mapping since element x in set P is associated with two elements m, n of set Q.<\/p>\n
\n
\n(a) f(0)
\n(b) f(-3)
\n(c) f(4)
\n(d) f(-2)<\/p>\nSolution:<\/summary>\n
\n(a) f(0)
\nTo find the f(0), substitute 0 in the place of the x.
\nThe given equation is f(x) = 3x – 5
\nf(0) = 3 (0) – 5 = 0 – 5 = -5
\nf(0) = -5<\/p>\n
\nTo find the f(-3), substitute -3 in the place of the x.
\nThe given equation is f(x) = 3x – 5
\nf(-3) = 3 (-3) – 5 = -9 – 5 = -14
\nf(-3) = -14<\/p>\n
\nTo find the f(4), substitute 4 in the place of the x.
\nThe given equation is f(x) = 3x – 5
\nf(4) = 3 (4) – 5 = 12 – 5 = 7
\nf(4) = 7<\/p>\n
\nTo find the f(-2), substitute -2 in the place of the x.
\nThe given equation is f(x) = 3x – 5
\nf(-2) = 3 (-2) – 5 = -6 – 5 = -11
\nf(-2) = -11<\/p>\n
\n
\n(a) f(x) = 7 – x, x \u2208 N, x > 0
\n(b) f(x) = x\u00b2 + 4, x \u2208 R<\/p>\nSolution:<\/summary>\n
\nx > 0
\nMultiply -1 on both sides.
\n– x < 0
\nAdd 7 on both sides
\n7 – x < 0 + 7
\n7 – x < 7
\nWe know that f(x) = 7 – x
\nf(x) < 7
\nWe know that value of f(x) is less than 7<\/p>\n
\nx\u00b2 \u2265 0
\nAdd 4 on both sides.
\nx\u00b2 + 4 \u2265 0 + 4
\nx\u00b2 + 4 \u2265 4
\nWe know that f(x) = x\u00b2 + 4
\nf(x) \u2265 4<\/p>\n
\n
\nConsider the rule f(x) = x + 3, where x \u2208 A.
\nRepresent the mapping in the roster form.
\nAlso, find the domain and range of the mapping.<\/p>\nSolution:<\/summary>\n
\nConsider the rule f(x) = x + 3, where x \u2208 A.
\nFor the required Relation we have to find the ordered pairs where x co-ordinate is from set M which is mapped to the y co-ordinate from set N.
\nIf f(2) = 2 + 3 = 5
\nf(4) = 4 + 3 = 7
\nf(7) = 7 + 3 = 10
\nf(8) = 8 + 3 = 11
\nA set of ordered pairs r = {(2, 5); (4, 7); (7, 10); (8, 11)}
\nDomain = Set of all first elements in a relation = {2, 4, 7, 8}
\nRange = Set of all second elements in a relation = {5, 7, 10, 11}<\/p>\n<\/details>\n
\n
\nDraw the arrow diagram to represent the rule f(x) = 2x from A to B.<\/p>\nSolution:<\/summary>\n
\nConsider the rule f(x) = 2x from A to B
\nFor the required Relation we have to find the ordered pairs where x co-ordinate is from set A which is mapped to the y co-ordinate from set B.
\nIf f(2) = 2 (2) = 4
\nf(3) = 2 (3) = 6
\nf(6) = 2 (6) = 12
\nA set of ordered pairs r = {(2, 4); (3, 6); (6, 12)}
\n![\"Functions](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Functions-or-Mapping-Worksheet-problems-with-answers.jpg\")
<\/p>\n<\/details>\n
\n
\n(a) Show that the relation R = {(4, 2), (9, 3)} is not a mapping from A to B.
\n(b) Show that the relation R = {(4, 2); (4, 4); (9, 3); (12, 2); (12, 4)} from A to B is not a mapping from A to B.<\/p>\nSolution:<\/summary>\n
\n(a) R = {(4, 2), (9, 3)} is not a mapping from A to B.
\nEvery element of A must have an image in B. From the given information, set A element 12 is not associated with any element of set B.<\/p>\n
\nNo element of A must have more than one image. From the given information, set A elements 4 and 12 are associated with two elements of set B. Element 4 of Set A associated with 2 and 4. Also, the 12 of Set A associated with 2 and 4.<\/p>\n
\n
\nConsider the rule f(x) = 5x – 3, where x \u2208 A
\n(a) Show that f is a mapping from A to B.
\n(b) Find the domain and range of the mapping.
\n(c) Represent the mapping in the roster form.
\n(d) Draw the arrow diagram to represent the mapping.<\/p>\nSolution:<\/summary>\n
\n(a) If f(x) = 5x – 3, where x \u2208 A
\nSubstitute elements of A in f(x)
\nf(3) = 5 (3) – 3 = 12
\nf(4) = 5 (4) – 3 = 17
\nf(5) = 5 (5) – 3 = 22
\nDifferent elements of A can have the same image in B. Adjoining figure represents a mapping.<\/p>\n
\nRange = Set of all second elements in a relation = {12, 17, 22}<\/p>\n![\"Functions](\"https:\/\/www.worksheetsbuddy.com\/wp-content\/uploads\/2021\/04\/Functions-or-Mapping-Worksheet-problems-with-solutions.jpg\")
<\/p>\n<\/details>\n","protected":false},"excerpt":{"rendered":"