A-12 Answers to Selected Exercises 69. x y 2 0 4 g(x) = (x – 4)2 71. x y 9 6 –5 –2 1 4 g(x) = (x + 2)2 0 73. –2 2 x y g(x) = ∣ x∣ – 1 0 75. x y 2 –1 h(x) = –(x + 1)3 0 77. x y 1 0 1 h(x) = 2x2 – 1 79. x y 4 –4 2 f(x) = 2(x – 2)2 – 4 0 81. x y –2 0 2 2 f(x) = √x + 2 83. x y 0 –2 –2 4 2 f(x) = –√x 85. x y 0 1 4 1 5 f(x) = 2√x + 1 87. x y –2 4 g(x) = x3 – 4 1 2 0 89. x y 3 8 –3 0 g(x) = (x + 3)3 91. x y –1 2 2 f(x) = (x – 2) 2 2 3 0 93. (a) x y –3 2 2 y = g(–x) 0 The graph of g1x2 is reflected across the y-axis. (b) x y –3 3 2 –2 y = g(x – 2) 0 The graph of g1x2 is translated to the right 2 units. (c) x y 3 –3 1 –2 –4 0 y = –g(x) The graph of g1x2 is reflected across the x-axis. (d) x y 3 2 0 y = –g(x) + 2 The graph of g1x2 is reflected across the x-axis and translated up 2 units. 95. It is the graph of ƒ1x2 = x translated to the left 1 unit, reflected across the x-axis, and translated up 3 units. The equation is y = - x + 1 + 3. 97. It is the graph of g1x2 = 1x translated to the right 1 unit and translated down 3 units. The equation is y = 1x - 1 - 3. 99. It is the graph of g1x2 = 1x translated to the left 4 units, stretched vertically by a factor of 2, and translated down 4 units. The equation is y = 21x + 4 - 4. 101. ƒ1-32 = -6 103. ƒ192 = 6 105. ƒ1-32 = -6 107. g1x2 = 2x + 13 109. (a) x y 2 2 0 (b) x y 2 0 2 Chapter 2 Quiz [2.5] 1. (a) y = 2x + 11 (b) A - 11 2 , 0B 2. y = - 2 3 x 3. (a) x = -8 (b) y = 5 [2.6] 4. (a) cubing function; domain: 1-∞, ∞2; range: 1-∞, ∞2; increasing over 1-∞, ∞2 (b) absolute value function; domain: 1-∞, ∞2; range: 30, ∞2; decreasing over 1-∞, 02; increasing over 10, ∞2 (c) cube root function; domain: 1-∞, ∞2; range: 1-∞, ∞2; increasing over 1-∞, ∞2 5. $2.75 6. x y 3 0 1 4 2x + 3 if x * 0 f(x) = √x if x # 0 [2.7] 7. x y 1 9 –1 –7 f(x) = –x3 + 1 8. f(x) = 2zx – 1z + 3 x y 3 5 0 1 9. g1x2 = -1x + 4 - 2 10. (a) even (b) neither (c) odd 2.8 Exercises 1. 7 3. 12 5. 5 7. 1-∞, ∞2 9. 1-∞, ∞2 11. 12 13. -4 15. - 38 17. 1 2 19. 5x - 1; x + 9; 6x2 - 7x - 20; 3x + 4 2x - 5 ; All domains are 1-∞, ∞2 except for that of ƒ g , which is A -∞, 5 2B ´A 5 2 , ∞B . 21. 3x2 - 4x + 3; x2 - 2x - 3; 2x4 - 5x3 + 9x2 - 9x; 2x2 - 3x x2 - x + 3 ; All domains are 1-∞, ∞2. 23. 24x - 1 + 1 x ; 24x - 1 - 1 x ; 24x - 1 x ; x 24x - 1; All domains are C 1 4 , ∞B . 25. 360; 580; 940 (all in thousands) 27. 2006–2011 29. 8; It represents the dollars (in billions) spent for general science in 2003. 31. general science; 2011–2019
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