(2 ) (4x 57. 4sec 3cos + 2) + 1 x y 60. = = y The graph of = sec is stretched vertically by The graph of = cos is shifted left 2 units, y x y x a factor of 4 and compressed horizontally by a factor of 1 . compressed horizontally by a factor of 1 , 4 2 y stretched vertically by a factor of 3, and shifted 4 (0, 4) ( , 4) up 1 unit. 3 ( , 4) 2 1 4 3 3 ––– 4 x –3– – – – 4 4 2 – – ( 4) 4 – –, (––, 5 4) 58. = ⎛ + π ⎞ csc y x ⎜ ⎟ 4 π ⎛ ⎞ x ⎝ ⎠ 61. = 4 tan ⎜ + ⎟ y The graph of ⎝ 2 4 ⎠ π = csc is shifted units to the y x 4 The graph of = tan is stretched horizontally y x (2x = 4sin + 4) − 2 y by a factor of 2, shifted left units, and π 4 59. stretched vertically by a factor of 4. left. The graph of = ⎛ − π ⎞ 5cot y x = sin is shifted left 4 units, y x 62. compressed horizontally by a factor of 1 , ⎝ 3 4 ⎠ 2 stretched vertically by a factor of 4, and shifted = cot is shifted right units, π y x The graph of 4 down 2 units. stretched horizontally by a factor of 3, and stretched vertically by a factor of 5.
57. y = 4sec (2 x ) 60. y = 3cos (4x + 2) + 1 The graph of y = sec x is stretched vertically by The graph of y = cos x is shifted left 2 units, a factor of 4 and compressed horizontally by a factor of 1 . compressed horizontally by a factor of 1 , 4 2 ( , 4) y 4 (0, 4) ( , 4) 3 2 1 stretched vertically by a factor of 3, and shifted up 1 unit. 3 ––– 4 – – 4 2 3 – – 4 –3– – x 4 ( – –, 4) 4 5 (––, 4) 58. y = csc ⎛ x + π ⎞ ⎜ 4 ⎟ ⎛ x π ⎞ ⎝ ⎠ 61. y = 4 tan ⎜ + ⎟ The graph of y = csc x is shifted π units to the ⎝ 2 4 ⎠ 4 The graph of y = tan x is stretched horizontally 59. left. y = 4sin (2x + 4) − 2 by a factor of 2, shifted left π units, and 4 stretched vertically by a factor of 4. The graph of y = sin x is shifted left 4 units, 62. y = 5cot ⎛ x − π ⎞ compressed horizontally by a factor of 1 , ⎝ 3 4 ⎠ 2 stretched vertically by a factor of 4, and shifted The graph of y = cot x is shifted right π units, 4 down 2 units. stretched horizontally by a factor of 3, and stretched vertically by a factor of 5.