A-10 Answers to Selected Exercises 11. 1x - 222 + 1y + 122 = 9 x y 0 2 3 12. x2 + 1y - 222 = 4 x y 2 2 5 –2 0 2 43. slope: 3 2 ; y-intercept: 10, 12 x y –2 2 0 y – x – 1 = 0 3 2 – 2 3 45. (a) -2; 10, 12; A1 2 , 0B (b) ƒ1x2 = -2x + 1 47. (a) - 1 3 ; 10, 22; 16, 02 (b) ƒ1x2 = - 1 3 x + 2 49. (a) -200; 10, 3002; A3 2 , 0B (b) ƒ1x2 = -200x + 300 51. (a) x + 3y = 11 (b) y = - 1 3 x + 11 3 53. (a) 5x - 3y = -13 (b) y = 5 3 x + 13 3 55. (a) y = 1 (b) y = 1 57. (a) y = 6 (b) y = 6 59. (a) - 1 2 (b) - 7 2 61. (a) y = 183.5x + 8070 (b) $8621; The result is $157 less than the actual figure. 63. (a) ƒ1x2 = 1238.75x + 24,523 f(x) = 1238.75x + 24,523 −4000 −1 35,000 5 To the nearest dollar, the average annual increase in tuition and fees is $1239 per year for this period because this is the slope of the line. (b) ƒ132 = $28,239; This is a fairly good approximation. (c) ƒ1x2 = 1214.5x + 24,448.8 65. (a) F = 9 5 C + 32 (b) C = 5 9 1F - 322 (c) -40° 67. (a) C = 0.8863I - 1530 (b) 0.8863 69. 536 71. 5-0.56 73. (a) 5126 (b) The solution does not appear in the x-values interval 3-10, 104. The minimum and maximum values must include 12. 75. collinear 77. not collinear 79. 2x1 2 + m1 2x 1 2 80. 2x 2 2 + m2 2x 2 2 81. 21x2 - x122 + 1m2x2 - m1x122 83. -2x1x21m1m2 + 12 = 0 84. Because x1 ≠0, x2 ≠0, we have m1m2 + 1 = 0, implying that m1m2 = -1. 85. If two nonvertical lines are perpendicular, then the product of the slopes of these lines is -1. Summary Exercises on Graphs, Circles, Functions, and Equations 1. (a) 265 (b) A5 2, 1B (c) y = 8x - 19 2. (a) 229 (b) A3 2 , -1B (c) y = - 2 5 x - 2 5 3. (a) 5 (b) A 1 2 , 2B (c) y = 2 4. (a) 110 (b) Q3 12 2 , 2 22 R (c) y = -2x + 512 5. (a) 2 (b) 15, 02 (c) x = 5 6. (a) 412 (b) 1-1, -12 (c) y = x 7. (a) 413 (b) A423, 325 B (c) y = 315 8. (a) 234 (b) A3 2 , - 3 2B (c) y = 5 3 x - 4 9. y = - 1 3 x + 1 3 x y 1 4 –2 0 10. y = 3 x y 3 0 13. y = - 5 6 x - 5 2 x y –5 –3 3 0 14. x = -4 x y –4 0 15. y = - 2 3 x x y –3 2 0 16. y = - 4 3 x x y 3 –4 0 17. yes; center: 12, -12; radius: 3 18. no 19. yes; center: 16, 02; radius: 4 20. yes; center: 1-1, -82; radius: 2 21. no 22. yes; center: 10, 42; radius: 5 23. A4 - 27, 2B, A4 + 27, 2B 24. 8 25. (a) domain: 1-∞, ∞2; range: 1-∞, ∞2 (b) ƒ1x2 = 1 4 x + 3 2 ; 1 26. (a) domain: 3-5, ∞2; range: 1-∞, ∞2 (b) y is not a function of x. 27. (a) domain: 3-7, 34; range: 3-5, 54 (b) y is not a function of x. 28. (a) domain: 1-∞, ∞2; range: C - 3 2 , ∞B (b) ƒ1x2 = 1 2 x 2 - 3 2 ; 1 2 2.6 Exercises 1. E; 1-∞, ∞2 3. A; 1-∞, ∞2 5. F; ƒ1x2 = x 7. H; no 9. B; 5. . . , -3, -2, -1, 0, 1, 2, 3, . . . 6 11. 1-∞, ∞2 13. 30, ∞2 15. 1-∞, 32; 13, ∞2 17. (a) -10 (b) -2 (c) -1 (d) 2 19. (a) -3 (b) 1 (c) 0 (d) 9 21. x y 2 –1 3 f(x) = x – 1 if x " 3 2 if x + 3 0 23. x y 5 4 2 f(x) = 4 – x if x * 2 1 + 2x if x # 2 0 25. x y 3 –2 –4 1 f(x) = –3 if x " 1 –1 if x + 1 0 27. y x 4 18 –4 2 + x if x * –4 –x if –4 " x " 5 3x if x + 5 f(x) = –2 0
RkJQdWJsaXNoZXIy NjM5ODQ=