51. = + 54. = tan( 4 tan(2x) y x y π) The graph of The graph of π = tan is stretched vertically by = y x tan is shifted units to the y x =− ⎛ − π ⎞ tan y x a factor of 4 and compressed horizontally by a factor of 1 . 52. 2 left. ⎜ ⎟ 2 ⎝ ⎠ 55. = π = cot ⎛ + π ⎞ tan is shifted units to the The graph of y x y x 2 ⎜ 4 ⎟ ⎝ ⎠ right and reflected across the x-axis. π shifted units to the 4 = cot is y x The graph of left. 53. = − 2 tan(3x) y The graph of 56. = − 4 cot(2 y x) = tan is stretched vertically by y x a factor of 2, reflected across the and x-axis, The graph of = cot is stretched vertically by y x compressed horizontally by a factor of 1 . 3 a factor of 4, reflected across the and x-axis compressed horizontally by a factor of 1 . 2
51. y = tan( x + π) 54. y = 4 tan(2x) The graph of y = tan x is shifted π units to the The graph of y = tan x is stretched vertically by 52. left. y =− tan ⎛ x − π ⎞ a factor of 4 and compressed horizontally by a factor of 1 . 2 ⎜ 2 ⎟ ⎝ ⎠ The graph of y = tan x is shifted π units to the 55. y = cot ⎛ x + π ⎞ 2 ⎜ 4 ⎟ ⎝ ⎠ right and reflected across the x-axis. The graph of left. y = cot x is shifted π units to the 4 53. y = − 2 tan(3x) The graph of y = tan x is stretched vertically by 56. y = − 4 cot(2 x) a factor of 2, reflected across the x-axis, and The graph of y = cot x is stretched vertically by compressed horizontally by a factor of 1 . 3 a factor of 4, reflected across the x-axis and compressed horizontally by a factor of 1 . 2
62514-0132318806_ISM_02-1.docx