A-7 Answers to Selected Exercises Chapter 2 Graphs and Functions 2.1 Exercises 1. II 3. 0 5. 15, 02 7. true 9. false; The midpoint is a point with coordinates 12, 22. 11. any three of the following: 12, -52, 1-1, 72, 13, -92, 15, -172, 16, -212 13. any three of the following: 12007, 20.02, 12009, 19.52, 12011, 18.12, 12013, 15.72, 12015, 10.82, 12017, 8.82 15. (a) 13 (b) A1, - 7 2B 17. (a) 234 (b) A11 2 , 7 2B 19. (a) 3241 (b) A0, 5 2B 21. (a) 2133 (b) Q212 , 3 15 2 R 23. yes 25. no 27. yes 29. yes 31. no 33. no 35. 1-3, 62 37. 15, -42 39. 12a - p, 2b - q2 41. 29.7%; This estimate is 0.3% more than the actual figure. 43. $24,676 Other ordered pairs are possible in Exercises 47–57. 47. (a) x y 0 -2 4 0 2 -1 (b) x y –2 4 0 y = x – 2 1 2 49. (a) x y 0 5 3 5 2 0 4 -1 (b) x y 2x + 3y = 5 5 2 5 3 0 51. (a) (b) x y 0 0 1 1 -2 4 x y 4 –2 0 2 y = x2 53. (a) x y 3 0 4 1 7 2 (b) x y 2 3 7 y = √x – 3 0 55. (a) x y 4 2 -2 4 0 2 (b) x y 4 –2 –2 2 4 y = zx – 2z 0 57. (a) x y 0 0 -1 -1 2 8 (b) x y 2 8 y = x3 59. 14, 02 61. III; I; IV; IV 63. yes; no 2.2 Exercises 1. 10, 02; 7 3. 14, -72 5. B 7. D 9. one (The point is 10, 02.) 11. (a) x2 + y2 = 36 (b) 13. (a) 1x - 222 + y2 = 36 (b) 15. (a) x2 + 1y - 422 = 16 (b) 17. (a) 1x + 222 + 1y - 522 = 16 (b) 19. (a) 1x - 522 + 1y + 422 = 49 (b) 21. (a) Ax - 22 B 2 + Ay - 22 B 2 = 2 (b) x y (0, 0) 6 6 6 x2 + y2 = 36 x y (2, 0) 8 6 (x – 2)2 + y2 = 36 0 x y (0, 4) –4 0 4 4 x2 + ( y – 4)2 = 16 x y 2 4 (–2, 5) 9 (x + 2)2 + (y – 5)2 = 16 0 x y –2 3 7 (5, –4) (x – 5)2 + (y + 4)2 = 49 0 x y ( x – √2 )2 + ( y – √2 )2 = 2 √2 ( , ) √2 0 √2
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