41, 43, 49, 51, 53, 55, 57, 59 solve on graph paper
ale NOTE many China .4 against in routed to the ste emners already vote state and xperienced my person said with prosthetics is a strong smell. .n7 I was pre packed me some Mes. The aroma fill actually, literally hey pulled ese "friends" . refusing to volleyball practice ward to the runs an In. "CHINK"! I look in short, "Go back to West rose with the B the yellow peril,' an mely surprised to see a. Stop eating dogs! thought that everyone , offense", ild have rigonometry RCISES Section 4.5 Graphs of Sir apha of si e blanks. See www.CalcChat.com for worked out solutions to add-numbered exert cosine function is called one of the sine or cosine curve. 35. /(x) = - - sin 36. /(x) = 4 sin #x or cosine curve represents half the distance between the maximum and minimum values GRAPHICAL REASONIN ASONIN g(x) = 3 - - sin d for the function f(x) = g(x) = 4 sin TX - 3 f matches the figure. sure y y = a sin(bx - c). * represents the of the graph of the function. 37. f(x) = 2 cost 38. (x) = -205 X y = d + a cos(bx - c). d represents a of the graph of the function. g(x) = 2 cos(x + 5) - COSlx - #) INS In Exercises 39-60, sketch the graph of the function. (Include two full periods.) iod and amplitude. In Exercises 19-26, describe the relationship between the 39. y = 5 sin x 40. y = _ sin x 6. y = 3 cos 2x graphs of f and g. Consider amplitude, period, and shifts 41. y = 3 COS .X 42. y = 4 cos x 75. 19. f(x) = sin x 20. f(x) = Cos x 13. y = Cos 44. y = sin 4x g(x) = sin(x - #) g(x) = cos(x + +7) 21. f(x) = cos 2x 22. f(x) = sin 3x 45. y = cos 2 TX 46. y = sin- (r) = - cos 2x g(x) = sin(-3x) 23. f(x) - cos x 24. f(x) = sin x 47. y= - 18. y = - 10 cos 6 g(x) = cos 2x g(x) = sin 3x L HEASO 25. f(x) = sin 2x 26. f(x) = cos 4x 49. y = sin x - 50. y = sin(x - 2x) GRAPHICAL REASO and c for the funct he functi y = -3 sin = g(x) = 3 + sin 21 graph of f matches th hatches th g(x) = -2+ cos 4x. $1. y = 3 cos(x + #) 52. y = 4 cos( x + 7) TT. In Exercises 27-30, describe the relationship between the graphs of f and g. Consider amplitude, period, and shifts. 53. y = 2 - sin 54. y = -3 + 5 cos 27 28. 55. y = 2 + 10 COS 60TX 56. y = 2 cos x - 3 57. y = 3 cos(x + ) - 3 58. y = 4 cos( x + #) + 4 AAMA 59. y = = 005( - 60. y = -3 cos(x + #) 79 7 cos - 3+ In Exercises 61-66, & is related to a parent function 29 30. f(x) = sin(x) or f(x) = cos(x). (a) Describe the sequence of transformations from f to g. (b) Sketch the graph of g. (c) Use function notation to write g in terms of f. -3 61. g(x) = sin(4x - 7) 62. g(x) = sin(2+ + #) -27 63. g(x) = cos(x - w) + 2 64. g(x) = 1 + cos(x + #) In Exercises 81 at ises 81 at e intervi 65. g(x) = 2 sin(4x - 7) - 3 66. g(x) = 4 - sin(2x + w) yz in the interva 2x numbers x such s x such - COS In Exercises 31-38, graph f and g on the same set of In Exercises 67-72, use a graphing utility to graph the 81. y, = sin x = sin x s sin or coordinate axes. (Include two full periods.) function. Include two full periods. Be sure to choose an appropriate viewing window. S 31. f(x) = -2 sin .x 32. f(x) = sin x 67. y = -2 sin(4x + #) 68. y = -4 sin(=x - =) In Exercises 83- rises 83- described by th bed by th g(x) = 4 sin x g(x) = sin - COS TX 69. y = cos 2 Tx - " ) + 1 83. A sine cu Sine cu 33. f(x) = cos x 34. f(x) = 2 cos 2x a right ph right ph g(x) = 2 + cos x I unit g(x) = - cos 4x 71. y = -0.1 sin( T.X + ) 72. y = 100 sin 120 TI
