A-11 Answers to Selected Exercises 63. (a) for 30, 44: y = 0.95x + 48.1; for 14, 74: y = 3.7x + 37.1 (b) ƒ1x2 = e 0.95x + 48.1 3.7x + 37.1 if 0 … x … 4 if 4 6x … 7 65. (a) 50,000 gal; 30,000 gal (b) during the first and fourth days (c) 45,000; 40,000 (d) 5000 gal per day 67. (a) ƒ1x2 = 0.80 Œ x 2œ if 6 … x … 18 (b) $3.20; $5.60 2.7 Exercises 1. 3 3. left 5. x 7. 2; 3 9. y 11. (a) B (b) D (c) E (d) A (e) C 13. (a) G (b) D (c) E (d) B (e) C (f) A (g) H (h) F (i) I 15. (a) E (b) C (c) D (d) A (e) B 29. 0 (2, 0) (–2, 0) (0, 2) y x f(x) = x if x + 2 1 2 1 2 – x2 + 2 if x " 2 31. 2 2 –10 –5 0 x y f(x) = 2x if –5 " x * –1 –2 if –1 " x * 0 x2 – 2 if 0 " x " 2 33. 0 1 4 –6 –2 f(x) = x3 + 3 if –2 " x " 0 x + 3 if 0 * x * 1 4 + x – x2 if 1 " x " 3 y x In Exercises 35–41, we give one of the possible rules, then the domain, and then the range. 35. ƒ1x2 = e -1 1 if x … 0 if x 70 ; 1-∞, ∞2; 5-1, 16 37. ƒ1x2 = e 2 -1 if x … 0 if x 71 ; 1-∞, 04 ´11, ∞2; 5-1, 26 39. ƒ1x2 = e x 2 if x … 0 if x 70 ; 1-∞, ∞2; 1-∞, 04 ´526 41. ƒ1x2 = e 23 x x + 1 if x 61 if x Ú 1 ; 1-∞, ∞2; 1-∞, 12 ´32, ∞2 43. 1 45. 3 47. 1 49. -4 51. 83 53. 2 –2 0 2 –2 x y f(x) = [[–x]] 1-∞, ∞2; 5. . . , -2, -1, 0, 1, 2, . . . 6 55. y x 1 3 f(x) = [[2x]] 0 1-∞, ∞2; 5. . . , -2, -1, 0, 1, 2, . . . 6 57. (a) $10.80 (b) $2.40 (c) $0.60 59. x y 5 4 3 2 1 0 1 2 3 4 5 Weight (in ounces) Number of Stamps 61. 0 204060 80 100 80 60 40 20 (20, 100) (70, 0) Time (in minutes) Water (in gallons) x y 17. x y –2 0 2 3 6 f(x) = 3∣ x∣ 19. x y 2 3 0 –3 f(x) = ∣ x∣ 2 3 21. x y 8 –2 0 2 g(x) = 2x2 23. x y 2 –2 0 2 g(x) = x 1 ² 2 25. x y –2 2 –5 f(x) = – x 1 2 2 0 27. x y –2 –6 2 f(x) = –3zxz 0 29. x y 2 –2 –2 0 2 h(x) = ∣ – x∣ 1 2 31. x y 4 0 1 4 h(x) = √4x 33. x y 0 –4 –1 –2 f(x) = –√–x 35. (a) 14, 122 (b) 18, 162 37. (a) 12, 122 (b) 132, 122 39. x y 0 (c) (a) (b) (5, –3) 41. x y 0 (a) (c) (b) (–4, –2) 43. x = 2 45. y-axis 47. x-axis, y-axis, origin 49. origin 51. none of these 53. x-axis, y-axis, origin 55. y-axis 57. odd 59. even 61. neither 63. odd 65. x y 3 2 f(x) = x2 – 1 0 67. x y 0 2 2 6 –2 f(x) = x2 + 2
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