A-14 Answers to Selected Exercises [2.5] 10. (a) x = 5 (b) y = -3 11. (a) y = -3x + 9 (b) y = 1 3 x + 7 3 [2.3] 12. (a) 12, ∞2 (b) 10, 22 (c) 1-∞, 02 (d) 1-∞, ∞2 (e) 1-∞, ∞2 (f) 1-1, ∞2 [2.6, 2.7] 13. y x 1 1 f(x) = ∣ x – 2∣ – 1 3 0 14. x y 0 1 1 –3 f(x) = [[x + 1]] 15. x y 0 3 4 –2 f(x) = 3 if x * –2 2 – x if x # –2 1 2 16. (a) x y (0, 2) (4, 2) (1, –1) y = f(x) + 2 0 (b) x y (–2, 0) (2, 0) (–1, –3) y = f(x + 2) 0 (c) x y (0, 0) (4, 0) (1, 3) y = –f(x) 0 (d) x y (0, 0) (–4, 0) (–1, –3) y = f(–x) 0 (e) x y (0, 0) (4, 0) (1, –6) y = 2f(x) 0 17. It is translated to the left 2 units, stretched vertically by a factor of 2, reflected across the x-axis, and translated down 3 units. 18. (a) yes (b) yes (c) yes [2.8] 19. (a) 2x2 - x + 1 (b) 2x 2 - 3x + 2 -2x + 1 (c) A -∞, 1 2B ´A 1 2 , ∞B (d) 4x + 2h - 3 (e) 0 (f) -12 (g) 1 20. 12x - 6; C 3, ∞B 21. 21x + 1 - 7; C -1, ∞B [2.4] 22. (a) C1x2 = 3300 + 4.50x (b) R1x2 = 10.50x (c) R1x2 - C1x2 = 6.00x - 3300 (d) 551 figures 69. x y 0 –3 3 –3 f(x) = zxz – 3 71. y x 0 2 3 –1 –6 2 –3 –1 f(x) = –(x + 1)2 + 3 73. y x 0 1 2 3 4 5 1 –3 f(x) = [[x – 3]] 75. y x 0 2 –2 3 –4x + 2 if x " 1 3x – 5 if x + 1 f(x) = 77. y x 0 3 6 3 f(x) = z xz if x * 3 6 – x if x # 3 79. true 81. false; For example, ƒ1x2 = x2 is even, and 12, 42 is on the graph but 12, -42 is not. 83. true 85. x-axis 87. y-axis 89. none of these 91. y-axis 93. x-axis, y-axis, origin 95. Reflect the graph of ƒ1x2 = x across the x-axis. 97. Translate the graph of ƒ1x2 = x to the right 4 units and stretch it vertically by a factor of 2. 99. y = -3x - 4 101. (a) y x (–4, 3) (4, 1) (8, 3) –4 4 5 8 0 (b) y x (–2, 0) (6, –2) (10, 0) –4 –2 4 2 10 0 (c) y x (–7, –2) (1, –4) (5, –2) –3 –4 5 0 (d) y x (–4, 0) (4, 2) (8, 0) 2 0 103. 3x4 - 9x3 - 16x2 + 12x + 16 105. 68 107. - 23 4 109. 1-∞, ∞2 111. 2 113. x - 2 115. 1 117. undefined 119. 8 121. -6 123. 2 125. 1 127. ƒ1x2 = 36x; g1x2 = 1760x; 1ƒ∘ g21x2 = ƒ1g1x22 = ƒ11760x2 = 3611760x2 = 63,360x 129. V1r2 = 4 3 p1r + 323 - 4 3 pr 3 Chapter 2 Test [2.3] 1. (a) D (b) D (c) C (d) B (e) C (f) C (g) C (h) D (i) D (j) C [2.4] 2. 3 5 [2.1] 3. 134 4. A1 2 , 5 2B [2.5] 5. 3x - 5y = -11 6. ƒ 1x2 = 3 5 x + 11 5 [2.2] 7. (a) x2 + y2 = 4 (b) 1x - 122 + 1y - 422 = 1 8. (–2, 5) x y 5 –2 4 0 x2 + y2 + 4x – 10y + 13 = 0 [2.3] 9. (a) not a function; domain: 30, 44; range: 3-4, 44 (b) function; domain: 1-∞, -12 ´1-1, ∞2; range: 1-∞, 02 ´10, ∞2; decreasing over 1-∞, -12 and 1-1, ∞2 Chapter 3 Polynomial and Rational Functions 3.1 Exercises 1. 5 3. vertex 5. -1 7. C 9. D 11. (a) domain: 1-∞, ∞2; range: 3-4, ∞2 (b) 1-3, -42 (c) x = -3 (d) 10, 52 (e) 1-5, 02, 1-1, 02 13. (a) domain: 1-∞, ∞2; range: 1-∞, 24 (b) 1-3, 22 (c) x = -3 (d) 10, -162 (e) 1-4, 02, 1-2, 02 15. B 17. D 19. x y 2 8 (b)(a) (c) 0 (d) The greater 0 a0 is, the narrower the parabola will be. The smaller 0 a0 is, the wider the parabola will be.
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