A-23 Answers to Selected Exercises 3. (–2, 11) x y 2 2 f(x) = –3x2 – 12x – 1 0 vertex: 1-2, 112; axis: x = -2; x-intercepts: Q-6 { 233 3 , 0R ; y-intercept: 10, -12; domain: 1-∞, ∞2; range: 1-∞, 114; increasing on 1-∞, -22; decreasing on 1-2, ∞2 5. 90 m by 45 m 7. (a) 120 (b) 40 (c) 22 (d) 84 (e) 146 (f) x 0 8 y 10 (8, 22) August The minimum occurs in August when x = 8. 9. x2 + 4x + 1 + -7 x - 3 11. 2x2 - 8x + 31 + -118 x + 4 13. 1x - 2215x2 + 7x + 162 + 26 15. -1 17. 28 19. yes 21. 7 - 2i In Exercises 23 –27, other answers are possible. 23. ƒ1x2 = x3 - 10x2 + 17x + 28 25. ƒ1x2 = x4 - 5x3 + 3x2 + 15x - 18 27. ƒ1x2 = x4 - 6x3 + 9x2 - 6x + 8 29. 1 2 , -1, 5 31. (a) ƒ1-12 = -10 60; ƒ102 = 2 70 (b) ƒ122 = -4 60; ƒ132 = 14 70 (c) 2.414 33. (a) The numbers in the bottom row of synthetic division are all positive. (b) The numbers in the bottom row of synthetic division alternate between positive and negative. 35. yes 37. ƒ1x2 = -2x3 + 6x2 + 12x - 16 39. 1, - 1 2 , {2i 41. 13 2 43. Any polynomial that can be factored into a1x - b23 satisfies the conditions. One example is ƒ1x2 = 21x - 123. x y 0 f(x) = 2(x – 1)3 1 1 45. (a) 1-∞, ∞2 (b) 1-∞, ∞2 (c) ƒ1x2 S∞ as x S∞, ƒ1x2 S-∞ as x S-∞: (d) at most seven (e) at most six 47. x y 20 5 2 –3 f(x) = (x – 2)2(x + 3) 0 49. x y 1 1 –1 0 f(x) = 2x3 + x2 – x 51. x y 4 2 –2 –4 0 f(x) = x4 + x3– 3x2 – 4x – 4 53. C 55. E 57. B 59. 7.6533119, 1, -0.6533119 f(x) = −0.0109x2 + 0.8693x + 11.85 10 0 40 40 f(x) = −0.00087x3 + 0.0456x2 − 0.2191x + 17.83 10 0 40 40 (e) Both functions approximate the data well. The quadratic function is probably better for prediction, because it is unlikely that the percent of out-of-pocket spending would decrease after 2025 (as the cubic function shows) unless changes were made in Medicare law. 63. 12 in. * 4 in. * 15 in. 65. x y 2 2 f(x) = x = 1 x – 1 4 0 67. y x f(x) = 6x x2 + x – 2 3 2 –2 x = –2 0 61. (a) 10 0 40 40 (b) ƒ1x2 = -0.0109x2 + 0.8693x + 11.85 (c) ƒ1x2 = -0.00087x3 + 0.0456x2 - 0.2191x + 17.83 (d) 69. x y –2 –4 0 8 –10 4 f(x) = y = x – 2 x = –2 x2 + 4 x + 2 71. x y f(x) = 1 –2 0 x2 + 1 –2 73. (a) x y 0 2 3 4 y = 1 x = 3 f(x) = (x – 2)(x – 4) (x – 3)2 (b) One possibility is ƒ1x2 = 1x - 221x - 42 1x - 322 . 75. ƒ1x2 = -3x + 6 x - 1 77. (a) C(x) = 0 0 100 100 6.7x 100 − x (b) $127.3 thousand 79. A -5, 1 2B 81. 1-2, 12 ´ 14, ∞2 83. 10, 22 85. 3-1, 24 87. 35 89. 0.75 91. 27 93. 33,750 units
RkJQdWJsaXNoZXIy NjM5ODQ=