20. = −3cot = ; The graph cot is stretched y x y x of vertically by a factor of 3 and reflected about the x-axis. y ( , 3) 15 – – x , 3 – – = cot is y x ( ) π 15 = cot ⎛ ⎞ ; The graph of x 4 24. y ⎜ 4 ⎟ ⎝ ⎠ 4 by a factor of . ⎛ π ⎞ tan ; The graph of π 21. x stretched = tan is y x = y ⎜ ⎟ 2 ⎝ ⎠ y horizontally compressed by a factor of 2 . π 5 y 4 (1, 1) x 2 4 (–2 , 1 3 3 ( ) 1, 1) 4 2 ( , 1) –1– x 5 ; The graph of 4 x 2 = sec is stretched y y x vertically by a factor of 2. = 25. (0, 2) y 22. = tan is y x 4 = tan ⎛ 1 ⎞ ; The graph of y x ⎜ ⎟ 2 (2 , 2) ( , 2) 2) ⎝ ⎠ horizontally stretched by a factor of 2. y x ( , (– 8 1) , 4 – x = 1 csc ; The graph y x of 3 3 26. 2 2 2
20. y = −3cot x ; The graph of y = cot x is stretched vertically by a factor of 3 and reflected about the x-axis. y 15 ( – – , 3) x – – , 3 15 ( 4 ) 24. y = cot ⎛ π x ⎞ ; The graph of y = cot x is ⎜ 4 ⎟ ⎝ ⎠ 4 21. y = tan ⎛ π x ⎞ ; The graph of y = tan x is stretched by a factor of . π ⎜ 2 ⎟ ⎝ ⎠ horizontally compressed by a factor of 2 . π y 4 y 5 (1, 1) x 4 2 ( –1– , 1) (–2 , 1 ) x 2 4 3 3 ( 1, 1) 5 2 4 25. y = x ; The graph of vertically by a factor of 2. (0, 2) y y = sec x is stretched 22. y = tan ⎛ 1 x ⎞ ; The graph of y = tan x is 4 ⎜ 2 ⎟ (2 , 2) ⎝ ⎠ horizontally stretched by a factor of 2. y ( , 2) x ( , 2) 8 (– – , 1) 4 x 3 3 2 2 26. y = 1 csc x ; The graph of 2