AN10 Answers: Chapter 2 51. y x 10 10 (28, 2) (8, 22) (21, 1) (1, 21) Domain: ( ) −∞∞, ; Range: ( ) −∞∞, 53. y x 6 5 (1, 5) (23, 5) (0, 21) (22, 21) (21, 23) Domain: ( ) −∞ ∞, ; Range: [ ) − ∞3, 55. y 8 x 8 (2, 1) (3, 3) (6, 5) Domain: [ )∞ 2, ; Range: [ )∞1, 57. y x 5 5 (24, 0) (0, 22) (21, 21) Domain: ( ] −∞, 0 ; Range: [ ) − ∞ 2, 59. y x 5 5 (0, 22) (22, 0) (21, 21) Domain: ( ) −∞∞, ; Range: ( ) −∞∞, 61. y x 5 5 (0, 2) (2, 2) (1, 0) Domain: ( ) −∞∞, ; Range: [ )∞ 0, 63. y x 5 5 1 2 , 1 1 2 , 21 2 Domain: ( ) ( ) −∞ ∪ ∞ , 0 0, Range: ( ) ( ) −∞ ∪ ∞ , 0 0, 65. (a) ( ) ( ) = + F x f x 3 y x 7 5 (0, 5) (2, 5) (4, 3) (24, 1) (b) ( ) ( ) = + G x f x 2 y x 5 3 (0, 2) (2, 0) (22, 2) (26, 22) (c) ( ) ( ) = − P x f x y x 5 5 (4, 0) (24, 2) (0, 22) (2, 22) (d) ( ) ( ) = + − H x f x 1 2 y x 3 4 (1, 0) (21, 0) (3, 22) (25, 24) (e) ( ) ( ) = Q x f x 1 2 y x 5 5 (0, 1) (2, 1) (4, 0) (24, 21) (f) ( ) ( ) = − g x f x y x 5 5 (0, 2) (22, 2) (24, 0) (4, 22) (g) ( ) ( ) = h x f x2 y x 5 5 (0, 2) (1, 2) (2, 0) (22, 22) 67. (a) ( ) ( ) = + F x f x 3 y x 5 P (P, 3) (2P, 3) , 2 P 2 2 P 2 , 4 (b) ( ) ( ) = + G x f x 2 y x 2.5 2P (P 2 2, 0) (2P 2 2, 0) (22, 0) P 2 2 2, 1 P 2 2 2 2, 21 (c) ( ) ( ) = − P x f x y x 2.5 P , 1 P 2 2 P 2 , 21 2P (d) ( ) ( ) = + − H x f x 1 2 y x 1 2P (P 2 1, 22) (2P 2 1, 22) (21, 22) P 2 2 1, 21 P 2 2 2 1, 23 (e) ( ) ( ) = Q x f x 1 2 y x 2.5 P ,P 2 2 1 2 2 P 2 1 2 , (2P, 0) (f) ( ) ( ) = − g x f x y x 2.5 P P 2 , 21 , 1 P 2 2 2P (g) ( ) ( ) = h x f x2 y x P 2.5 P 4 , 1 P 4 , 2 21 , 0 P 2 2 P 2 , 0 69. ( ) ( ) = + − f x x 1 1 2 y x 5 5 (22, 0) (0, 0) (21, 21) 71. ( ) ( ) = − − f x x 4 15 2 y x 7.5 9 (8, 1) (0, 1) (4, 215) 73. ( ) ( ) = − + f x x 2 3 1 2 y x 5 5 (4, 3) (3, 1) (2, 3) 75. ( ) ( ) = − + − f x x 3 2 5 2 y x 1 5 (22, 25) (23, 28) (21, 28) 77. (a) −7 and 1 (b) −3 and 5 (c) −5 and 3 (d) −3 and 5 79. (a) [ ] −3, 3 (b) [ ] 4, 10 (c) Decreasing on [ ] −1, 5 (d) Decreasing on [ ] −5, 1 81. (a) y x 2.5 2.5 (2, 0) (1, 1) (22, 1) (21, 1) (b) y x 2.5 2.5 (2, 0) (1, 1) (22, 0) (21, 1) 83. (a) ( ) −2, 2 (b) ( ) − 3, 5 (c) ( ) −1, 3 85. (a) y x 5 25 5 25 (b) y x 5 25 5 25 87. (a) y x 5 7 (6, 0) (3, 23) (0, 0) (b) 9 square units 89. (a) ° 72 F; ° 65 F (b) The temperature decreases by °2 to ° 70 F during the day and ° 63 F overnight. Time (hours after midnight) T t 76 72 68 64 60 0 5 Temperature (8F) 10152025 (c) The time at which the temperature adjusts between the daytime and overnight settings is moved to 1 hr sooner. It begins warming up at 5:00 am instead of 6:00 am, and it begins cooling down at 8:00 pm instead of 9:00 pm. Time (hours after midnight) Temperature (8F) T t 76 72 68 64 60 0 5 10152025 91. 8F 8C 320 (100, 212) (0, 32) 256 192 128 64 0 20 40 60 80100 8F K 320 (373, 212) (273, 32) 256 192 128 64 0 280 310 350 93. y x 9 5 c 5 22 c 5 0 c 5 3 95. [ ] 4, 8 97. The graph of ( ) = y f x 4 is a vertical stretch by a factor of 4. The graph of ( ) = y f x 4 is a horizontal compression by a factor of 1 4 . 99. 16 3 sq. units 101. The domain of ( ) = g x x is [ )∞ 0, . The graph of ( ) − g x k is the graph of g shifted k units to the right, so the domain of ( ) − g x k is [ )∞ k, . 102. = = − m b 3 5 ; 6 103. 3.11 mph 104. 15.75 gal 105. Intercepts: ( ) ( ) ( ) − − 0, 2, 0,2, 4,0; x-axis symmetry 106. { } ≠ ≠ − x x x 7, 2 107. 7 sec 108. { } xy x z 2 3 2 2 2 109. + + x h 6 3 2 110. ( ) ( ) + − + z z z 6 6 36 2
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