Section 6.6 AN49 29. (0, 4) (2P, 24) (22P, 24) y 16 x 5P x x k k Domain: , is an odd integer π { } ≠ y y y Range: 4 or 4 { } ≤− ≥ 31. 3 2 , 2 1 2 , 22 3 2 2 , 22 1 2 2 , 2 y 6 x 2.5 x x Domain: does not equal an integer { } y y y Range: 2 or 2 { } ≤− ≥ 33. (0, 1) (3P, 0) (P, 2) (23P, 2) y 10 x 5P x x k k Domain: 2 , is an odd integer π { } ≠ Range: , ( ) −∞∞ 35. 3 2 , 1 3 2 2 , 1 y 8 x 2.5 (0, 3) x x k k Domain: 3 4 , is an odd integer { } ≠ y y y Range: 1 or 3 { } ≤ ≥ 37. P 8 5 2 , 2 2 y 10 x P P 8 3 2 , 2P 2 (0, 22) π { } ≠ x x k k Domain: 4 , is an odd integer Range: , ( ) −∞∞ 39. y 10 x 5 (23, 1) (3, 23) (1, 1) (21, 23) x x k k Domain: , is an even integer { } ≠ y y y Range: 3 or 1 { } ≤− ≥ 41. 2 3 π 43. 6 3 π 45. f g x x tan 4 ( )( ) ( ) = P 16 , 1 y 1 x P 16 2 , 21 P 4 g f x x 4 tan ( )( ) = P 4 , 4 2, 4 P 4 2 P 22 y 5 x P 2 47. ( )( ) = − f g x x 2 cot y 5 x 2P g f x x cot 2 ( )( ) ( ) = − y 2.5 x P 49. (p, 21) (0, 0) p 4 , 1 p 2 , 0 3p 4 , 2Ï2 x 5 p 2 y x 2.5 p (b) 0 0 25 p 2 53. y 5 x y 5 tan x 3P 2 P 2 x 1 y 5 2cot 3P 2 y 5 x 51. (a) L 3 cos 4 sin 3sec 4csc θ θ θ θ θ ( ) = + = + 55. Vertical Asymptotes: x k ,π = k an integer Domain: x x k k , an integer π { } ≠ Range: { } ( ] ≤ −∞ y y 0 or , 0 59. y x 6 26 26 18 (0, 23) (4, 22) 60. , 0 4, ( ) ( ) −∞ ∪ ∞ 61. 5 62. + − x c 3 63. ( ) ( ) ( ) − − 0, 2, 3 2 ,0, 2,0 64. ( ) + + x 1 5 2 2 65. ) ⎡ ∞ ⎣ ⎢ 2 5 , 6.6 Assess Your Understanding (page 459) 1. phase shift 2. False 3. = Amplitude 4 π = Period π = Phase shift 2 P 2 , 0 P 4 , 24 5P 4 , 24 3P 2 , 0 7P 4 , 4 3P 4 , 4 2P y 5 x (P, 0) 5. Amplitude 2 = Period 2 3 π = Phase shift 6 π = − 5P 6 , 22 P 6 , 22 P 6 , 2 2 (0, 0) 2P 3 , 0 P 2 , 2 P 3 , 0 y 2.5 x P 7. Amplitude 3 = Period π = Phase shift 4 π = − P 2 , 3 2 P 4 , 0 2 (0, 23) (P, 23) 3P 4 , 0 P 4 , 0 P 2 , 3 y 5 x P 9. Amplitude 4 = Period 2 π = Phase shift 4 π = − P 4 , 2 2 P 8 , 22 2 P 4 , 2 P 2 , 26 P 8 , 22 3P 8 , 22 P 4 y 3 x (0, 26) 2 P 2 56. p q p pq q 5 2 25 10 4 2 2 2 4 ( )( ) − + + 57. Hazel: 4 hours; Gwyneth: 6 hours 58. 1, 3 { } − (c) ≈0.83 (d) ≈9.86 ft
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