A-24 Answers to Selected Exercises Chapter 3 Test [3.1] 1. x y –3 1 f(x) = –2x2 + 6x – 3 ( , ) 3 2 3 2 0 x-intercepts: Q-3 { 23 -2 , 0R Qor Q 3 { 23 2 , 0RR ; y-intercept: 10, -32; vertex: A3 2 , 3 2B ; axis: x = 3 2 ; 2. (a) 2.75 sec (b) 169 ft (c) 0.7 sec and 4.8 sec (d) 6 sec [3.2] 3. 3x2 - 2x - 5 + 16 x + 2 4. 2x2 - x - 5 5. 53 [3.3] 6. It is a factor. The other factor is 6x3 + 7x2 - 14x - 8. 7. -2, -3 - 2i, -3 + 2i 8. ƒ1x2 = 2x4 - 2x3 - 2x2 - 2x - 4 [3.3, 3.4] 9. (a) ƒ112 = 5 70; ƒ122 = -1 60 (b) Positive Negative Nonreal Complex 2 1 0 0 1 2 (c) 4.0937635, 1.8370381, -0.9308016 [3.4] 10. x y 0 g(x) = –2(x + 5)4 + 3 (–5, 3) f(x) = x4 To obtain the graph of g, translate the graph of ƒ to the left 5 units, stretch by a factor of 2, reflect across the x-axis, and translate up 3 units. domain: 1-∞, ∞2; range: A -∞, 3 2D ; increasing on A -∞, 3 2B ; decreasing on A3 2 , ∞B 11. C 12. x y 9 3 –1 f(x) = x3 – 5x2 + 3x + 9 0 13. x y 0 2 2 f(x) = 2x2(x – 2)2 14. x y 0 f(x) = –x3 – 4x2 + 11x + 30 3 10 30 –5 –2 15. ƒ1x2 = 21x - 2221x + 32, or ƒ1x2 = 2x3 - 2x2 - 16x + 24 [3.5] 16. x y 4 6 –4 2 –2 5 8 f(x) = x = 2 y = 3 3x – 1 x – 2 0 17. x y 2 –4 4 3 f(x) = x = –3 x = 3 y = 1 x2 – 1 x2 – 9 0 18. (a) y = 2x + 3 (b) 1-2, 02, A3 2 , 0B (c) 10, 62 (d) x = 1 18. (e) x y –2 6 3 0 3 f(x) = y = 2x + 3 x = 1 2x2 + x – 6 x – 1 [3.6] 19. 5-56´C - 3 4 , 4D 20. 1-3, 02 ´33, ∞2 [3.7] 21. 60 22. 640 9 kg Chapter 4 Inverse, Exponential, and Logarithmic Functions 4.1 Exercises 1. one-to-one 3. one-to-one 5. range; domain 7. 23 x 9. -3 11. one-to-one 13. not one-to-one 15. one-to-one 17. one-to-one 19. not one-to-one 21. one-to-one 23. one-to-one 25. one-to-one 27. not one-to-one 29. one-to-one 31. not one-to-one 33. one-to-one 35. no 37. inverses 39. not inverses 41. inverses 43. not inverses 45. inverses 47. inverses 49. not inverses 51. 516, -32, 11, 22, 18, 526 53. not one-to-one 55. inverses 57. not inverses 59. (a) ƒ-11x2 = 1 3 x + 4 3 (b) x y 0 2 –4 2 –4 ƒ–1 ƒ (c) Domains and ranges of both ƒ and ƒ-1 are 1-∞, ∞2. 61. (a) ƒ-11x2 = - 1 4 x + 3 4 (b) x y –2 0 3 f f –1 (c) Domains and ranges of both ƒ and ƒ-1 are 1-∞, ∞2. 63. (a) ƒ-11x2 = 23 x - 1 (b) x y 0 ƒ–1 ƒ (c) Domains and ranges of both ƒ and ƒ-1 are 1-∞, ∞2. 65. not one-to-one 67. (a) ƒ-11x2 = 1 x , x ≠0 (b) x y 0 1 1 ƒ = ƒ–1 (c) Domains and ranges of both ƒ and ƒ-1 are 1-∞, 02 ´10, ∞2.
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