⎛ ⎞ + tan 1 1 ; The graph of x ⎛ 3π ⎞ ; The graph of 33. x 36. = y = tan is y x = csc is y x = y csc ⎜ ⎟ 4 ⎜ 2 ⎟ ⎝ ⎠ ⎝ ⎠ horizontally stretched by a factor of 4 and shifted 2 8 up 1 unit. y horizontally compressed by a factor of . 3π ( 3 , 2) ( , 2) (0, 1) (3 , 0)x 4 4 8 34. = 2 cot − 1 ; The graph = cot is y x y x of vertically stretched by a factor of 2 and shifted down 1 unit. 37. y = tan is y x = ⎛ ⎞ − 1 tan 1 2 ; The graph of y x 2 10 ⎜ ⎟ 4 ⎝ ⎠ ( 1) horizontally stretched by a factor of 4, vertically –3– –, 1 8 compressed by a factor of (– , 1) , and shifted down 2 – 2 units. 2 x – – ( y 2 , 1) – – 2 , 1 – – 2 ( 10 , –3– = sec ⎛ 2π ⎞ + 2 ; The graph y x 35. of 3 = sec is 3 y x x ⎜ ⎟ 3 ⎝ ⎠ ( 2) , –3– horizontally compressed by a factor of 3 and 2π 2 8 = cot is y x shifted up 2 units. = 3cot ⎛ 1 ⎞ − 2 ; The graph y x 38. of y 8 ⎜ 2 ⎟ ( 1) ,
33. y = tan ⎛ 1 x ⎞ + 1 ; The graph of y = tan x is 36. y = csc ⎛ 3π x ⎞ ; The graph of y = csc x is ⎜ 4 ⎟ ⎜ 2 ⎟ ⎝ ⎠ ⎝ ⎠ horizontally stretched by a factor of 4 and shifted 2 up 1 unit. y 8 horizontally compressed by a factor of . 3π ( 3 , 2) ( , 2) (0, 1) (3 , 0)x 4 4 8 34. y = 2 cot x − 1 ; The graph of y = cot x is vertically stretched by a factor of 2 and shifted down 1 unit. y 37. y = 1 tan ⎛ 1 x ⎞ − 2 ; The graph of y = tan x is 10 2 ⎜ 4 ⎟ ( –3– –, 1) ⎝ ⎠ horizontally stretched by a factor of 4, vertically 1 2 ( – – , 1) (– – , 1) – – x 2 2 compressed by a factor of units. y 8 , and shifted down 2 2 – – , 1 2 10 ( , –3– 35. y = sec ⎛ 2π x ⎞ + 2 ; The graph of y = sec x is 3 3 x ⎜ 3 ⎟ ⎝ ⎠ ( , –3– 2) horizontally compressed by a factor of 3 2π and 2 8 shifted up 2 units. y 8 38. y = 3cot ⎛ 1 x ⎞ − 2 ; The graph of y = cot x is ⎜ 2 ⎟ ( , 1)
62514-0132318806_ISM_02-1.docx