A-8 Answers to Selected Exercises 23. (a) 1x - 322 + 1y - 122 = 4 (b) x2 + y2 - 6x - 2y + 6 = 0 25. (a) 1x + 222 + 1y - 222 = 4 (b) x2 + y2 + 4x - 4y + 4 = 0 27. center: 1-3, -42; radius: 4 29. center: 12, -62; radius: 6 31. center: A - 1 2 , 2B ; radius: 3 33. center: A 1 3 , - 1 3B ; radius: 5 3 35. The graph is nonexistent. 37. The graph is the point 13, 32. 39. The graph is a circle with center 11, -62 and radius 7. 41. The graph is nonexistent. 43. 13, 12 45. 1-2, -22 47. 1x - 322 + 1y - 222 = 4 49. A2 + 27, 2 + 27 B , A2 - 27, 2 - 27 B 51. 12, 32 and 14, 12 53. 9 + 1119, 9 - 1119 55. 1113 - 5 57. 12, -32 58. 315 59. 315 60. 315 61. 1x - 222 + 1y + 322 = 45 62. 1x + 222 + 1y + 122 = 41 63. 1x - 522 + Ay - 9 2B 2 = 169 4 65. 1x - 322 + Ay - 5 2B 2 = 25 4 2.3 Exercises 1. 53, 4, 106 3. x; y 5. 10 7. 30, ∞2 9. 1-∞, 32 11. function 13. not a function 15. function 17. function 19. not a function; domain: 50, 1, 26; range: 5-4, -1, 0, 1, 46 21. function; domain: 52, 3, 5, 11, 176; range: 51, 7, 206 23. function; domain: 50, -1, -26; range: 50, 1, 26 25. function; domain: 52014, 2015, 2016, 20176; range: 570.7, 77.0, 84.2, 85.56 27. function; domain: 1-∞, ∞2; range: 1-∞, ∞2 29. not a function; domain: 33, ∞2; range: 1-∞, ∞2 31. function; domain: 1-∞, ∞2; range: 1-∞, ∞2 33. function; domain: 1-∞, ∞2; range: 30, ∞2 35. not a function; domain: 30, ∞2; range: 1-∞, ∞2 37. function; domain: 1-∞, ∞2; range: 1-∞, ∞2 39. not a function; domain: 1-∞, ∞2; range: 1-∞, ∞2 41. function; domain: 30, ∞2; range: 30, ∞2 43. function; domain: 1-∞, 02 ´10, ∞2; range: 1-∞, 02 ´10, ∞2 45. function; domain: C - 1 4 , ∞B ; range: 30, ∞2 47. function; domain: 1-∞, 32 ´13, ∞2; range: 1-∞, 02 ´10, ∞2 49. B 51. 4 53. -11 55. 3 57. 11 4 59. -3p + 4 61. 3x + 4 63. -3x - 2 65. -6m+ 13 67. (a) 2 (b) 3 69. (a) 15 (b) 10 71. (a) 3 (b) -3 73. (a) 0 (b) 4 (c) 2 (d) 4 75. (a) -3 (b) -2 (c) 0 (d) 2 77. (a) ƒ1x2 = - 1 3 x + 4 (b) 3 79. (a) ƒ1x2 =-2x2 - x + 3 (b) -18 81. (a) ƒ1x2 = 4 3 x - 8 3 (b) 4 3 83. 0.164 square unit 85. -4 87. (a) 1-2, 02 (b) 1-∞, -22 (c) 10, ∞2 89. (a) 1-∞, -22; 12, ∞2 (b) 1-2, 22 (c) none 91. (a) 1-1, 02; 11, ∞2 (b) 1-∞, -12; 10, 12 (c) none 93. (a) yes (b) 30, 244 (c) 1200 megawatts (d) at 17 hr or 5 p.m.; at 4 a.m. (e) ƒ1122 = 1900; At 12 noon, electricity use is 1900 megawatts. (f) increasing from 4 a.m. to 5 p.m.; decreasing from midnight to 4 a.m. and from 5 p.m. to midnight 95. (a) 12 noon to 8 p.m. (b) from midnight until about 6 a.m. and after 10 p.m. (c) about 10 a.m. and 8:30 p.m. (d) The temperature is 40° from midnight to 6 a.m., when it begins to rise until it reaches a maximum of just below 65° at 4 p.m. It then begins to fall until it reaches just under 40° at midnight. 97. The minimum value -2 occurs at x = 3, and the maximum value 2 occurs at x = -3. 99. The minimum value -3 occurs at x = 0, and the maximum value 3 occurs at x = -4 and x = 4. 2.4 Exercises 1. B 3. C 5. A 7. C 9. D In Exercises 11–29, we give the domain first and then the range. 11. 1-∞, ∞2; 1-∞, ∞2 x y 4 –4 f(x) = x – 4 0 13. x y –6 12 f(x) = x – 6 1 2 0 1-∞, ∞2; 1-∞, ∞2 15. x y 3 1 f(x) = 3x 0 1-∞, ∞2; 1-∞, ∞2 17. x y –4 f(x) = –4 0 1-∞, ∞2; 5-46; constant function 19. x y f(x) = 0 0 1-∞, ∞2; 506; constant function 21. x y 4 3 –4x + 3y = 12 0 1-∞, ∞2; 1-∞, ∞2 23. x y 4 3 3y – 4x = 0 0 1-∞, ∞2; 1-∞, ∞2 25. x y 3 x = 3 0 536; 1-∞, ∞2
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