4 1 a b y 1 y 2 1 1 0 1 x 2 1 c 1 2 d y y 1 1 2 2 1 x

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Unformatted text preview: 20 10 x -30 -20 -10 -10 10 20 x 30 —2 4 -20 —1 —1 -30 35. Plot f (x) on [−10, 10]; then on [−1, 0], [−0.7, −0.6], [−0.65, −0.64], [−0.646, −0.645]; for the other root use [4, 5], [4.6, 4.7], [4.64, 4.65], [4.645, 4.646]; roots −0.6455, 4.6455. 36. Plot f (x) on [−10, 10]; then on [−4, −3], [−3.7, −3.6], [−3.61, −3.60], [−3.606, −3.605]; for the other root use [3, 4], [3.6, 3.7], [3.60, 3.61], [3.605, 3.606]; roots 3.6055, −3.6055. EXERCISE SET 1.4 1. (a) (b) y -1 y 2 1 1 0 1 x 2 -1 (c) 1 2 (d) y y 1 -1 2. 2 1 x 2 -4 y (a) -2 2 1 x -2 2 y 3 y (d) 1 1 x 2 -1 x 2 y (b) x -2 (c) x 3 3 x -1 1 Exercise Set 1.4 3. 12 (a) y (b) 1 y 1 -2 -1 1 2 x -0.5 0.5 1 1.5 1 2 3 x -1 -1 (c) (d) y y 1 1 -1 1 2 3 x -1 x -1 -1 4. 5. Translate right 2 units, and up one unit. y y 1 -2 x 2 10 -2 6. Translate left 1 unit, reflect over x-axis, and translate up 2 units. 7. y 2 4 6 x Translate left 1 unit, stretch vertically by a factor of 2, reflect over x-axis, translate down 3 units. y -8 -6 -4 -2 2 4 6 x -20 x -40 1 -60 -80 –2 -100 8. Translate right 3 units, compress vertically by a factor of 1 , and translate up 2 units. 2 9. y = (x + 3)2 − 9; translate left 3 units and down 9 units. y y 15 10 5 -8 2 -6 -4 -2 2 -5 4 x x 13 10. Chapter 1 y = (x + 3)2 − 19; translate left 3 units and down 19 units. 11. y = −(x − 1)2 + 2; translate right 1 unit, reflect over x-axis, translate up 2 units. y y –4 x 2 x –5 -2 -1 1 2 3 4 -2 -4 -6 12. y = 1 [(x − 1)2 + 2]; translate left 1 unit 2 and up 2 units, compress vertically by a factor of 1 . 2 13. Translate left 1 unit, reflect over x-axis, translate up 3 units. y y 2 1 2 1 2 4 6 8 10 12 x x 1 14. Translate right 4 units and up 1 unit. 15. Compress vertically by a factor of 1 , 2 translate up 1 unit. y y 2 4 1 4 x 10 1 16. Stretch vertically by a factor of reflect over x-axis. √ 3 and 17. 2 3 x Translate right 3 units. y 10 y 2 x -1 2 -10 4 6 x Exercise Set 1.4 18. 14 Translate right 1 unit and reflect over x-axis. 19. Translate left 1 unit, reflect over x-axis, translate up 2 units. y y 12 10 8 6 4 2 2 x -2 2 -4 -3 -2 -1 -4 20. y = 1 − 1/x; reflect over x-axis, translate up 1 unit. 21. 1 -2 -4 -6 -8 x 2 Translate left 2 units and down 2 units. y y 5 -4 -2 x 2 x -2 -5 22. Translate right 3 units, reflect over x-axis, translate up 1 unit. 23. Stretch vertically by a factor of 2, translate right 1 unit and up 1 unit. y y 1 4 x 5 -1 2 x 2 24. y = |x − 2|; translate right 2 units. 25. Stretch vertically by a factor of 2, reflect over x-axis, translate up 2 units. y y 2 4 1 3 2 x 2 4 1 -2 2 -1 x 15 26. Chapter 1 Translate right 2 units and down 3 units. 27. Translate left 1 unit and up 2 units. y y x 2 3 2 –2 1 x -3 28. -2 -1 1 Translate right 2 units, reflect over x-axis. y 1 x 4 –1 29. y (a) (b) y = 2 0 if x ≤ 0 2x if 0 < x x -1 30. 1 y x 2 –5 31. x2 + 2x + 1, all x; 2x − x2 − 1, all x; 2x3 + 2x, all x; 2x/(x2 + 1), all x 32. 3x − 2 + |x|, all x; 3x − 2 − |x|, all x; 3x|x| − 2|x|, all x; (3x − 2)/|x|, all x = 0 33. √ √ 3 x − 1, x ≥ 1; x − 1, x ≥ 1; 2x − 2, x ≥ 1; 2, x > 1 34. (2x2 + 1)/x(x2 + 1), all x = 0; −1/x(x2 + 1), all x = 0; 1/(x2 + 1), all x = 0; x2 /(x2 + 1), all x = 0 35. (a) 3 (b) 9 (c) 2 (d) 2 36. (a) π − 1 (b) 0 (c) −π 2 + 3π − 1 (d) 1 Exercise Set 1.4 16 38. (a) t4 + 1 (b) t2 + 4t + 5 (c) x2 + 4x + 5 (e) x2 + 2xh + h2 + 1 37. (f ) x2 + 1 (g) x + 1 (a) (e) √ √ 4 5s + 2 (b) x √ √ (c) 3 5x √ (g) 1/ 4 x x+2 (f ) 0 1 +1 x2 (h) 9x2 + 1 (d) √ (d) 1/ x (h) |x − 1| 39. 2x2 − 2x +1, all x; 4x2 +2x, all x 41. 1 − x, x ≤ 1; 43. 1 1 1 1 , x = , 1; − − , x = 0, 1 1 − 2x 2 2x 2 44. 45. x−6 + 1 46. 47. (a) g (x) = 48. (a) g (x) = x + 1, h(x) = x2 (b) g (x) = 1/x, h(x) = x − 3 49. (a) g (x) = x2 , h(x) = sin x (b) g (x) = 3/x, h(x) = 5 + cos x 50. (a) g (x) = 3 sin x, h(x) = x2 (b) g (x) = 3x2 + 4x, h(x) = sin x 51. (a) f (x) = x3 , g (x) = 1 + sin x, h(x) = x2 (b) f (x) = 52. (a) f (x) = 1/x, g (x) = 1 − x, h(x) = x2 (b) f (x) = |x|, g (x) = 5 + x, h(x) = 2x 53. √ √ 1 − x2 , |x| ≤ 1 40. 2 − x6 , all x; −x6 + 6x4 − 12x2 + 8, all x 42. x2 x2 + 3 − 3, |x| ≥ x 1 , x = 0; + x, x = 0 +1 x x x+1 54. 1 -1 1 2 3 x -1 -2 -3 -4 55. Note that f (g (−x)) = f (−g (x)) = f (g (x)), so f (g (x)) is even. y f ( g(x)) 1 –3 1 –1 –1 –3 x √ {−2, −1, 0, 1, 2, 3} 2 -3 -2 √√ 6; x, x ≥ 3 (b) g (x) = |x|, h(x) = x2 − 3x + 5 x, h(x) = x + 2 y √ x, g (x) = 1 − x, h(x) = √ 3 x 17 56. Chapter 1 Note that g (f (−x)) = g (f (x)), so g (f (x)) is even. y 3 g( f (x)) 1 x –3 1 –1 3 –1 –2 57. f (g (x)) = 0 when g (x) = ±2, so x = ±1.4; g (f (x)) = 0 when f (x) = 0, so x = ±2. 58. f (g (x)) = 0 at x = −1 and g (f (x)) = 0 at x = −1 59. 6xh + 3h2 3(x + h)2 − 5 − (3x2 − 5) = = 6x + 3h h h 60. 2xh + h2 + 6h (x + h)2 + 6(x + h) − (x2 + 6x) = = 2x + h + 6 h h 61. 1/(x + h) − 1/x x − (x + h) −1 = = h xh(x + h) x(x + h) 62. 1/(x + h)2 − 1/x2 x2 − (x + h)2 2x + h =2 =− 2 h x h(x + h)2 x (x + h)2 63. (a) the origin 64. (a) (b) the x-axis (c) the y -axis (b) y (c) y x 65. (a) 66. x f (x) (a) −3 1 −2 −5 (d)...
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This document was uploaded on 02/23/2014 for the course MANAGMENT 2201 at University of Michigan.

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