−3csc ; The graph of 27. x = csc is 1 y x = y The graph of vertically stretched by a factor of 3 and reflected 2 = y about the x-axis. csc = csc is y x (2x 30. ) 1 ; a factor of y 2 14 3 vertically compressed by factor of 1 . (–––, 3) 10 2 ( , 3) 6 – – x y 2 ( , 3) – – 3 1.0 ––– 6 2 and by 10 ( , (––, ) 1 –3– – –1–) ) 4 2 –– 14 –1– – – ( , – – – – 2 x 2 4 2 28. = −4sec = (–3– ; The graph of sec is y x y x 4 2 –, –1–) 4 2 vertically stretched by a factor of 4 and reflected 1.0 about the x-axis. (π ) = −2 csc ; The graph y x 31. = csc is y x of horizontally compressed by a factor of 1 , π vertically stretched by a factor of 2, and reflected about the x-axis. y 6 29. = sec is ( y x = 4sec ⎛ 1 ⎞ ; The graph of 2) y x , 3 –– ⎜ 2 ⎟ 2 ⎝ ⎠ horizontally stretched by a factor of 2 and 2.0 1.0 1.0 2.0 x 1 –– vertically stretched by a factor of 4. 3 2 –– 2 y 36 6 32. = sec is y x π −3sec ⎛ ⎞ ; The graph of x (0, 4) = y ⎜ ⎟ 2 , ( 4) 4 2 2
27. y = −3csc x ; The graph of y = csc x is 1 vertically stretched by a factor of 3 and reflected about the x-axis. 30. y = csc (2x ) ; The graph of 2 y = csc x is 1 y 14 10 ( – – , 3) 6 2 3 ––– 2 6 3 (–––, 3) x ( – – , 3) by a factor of 2 vertically compressed by factor of 1 . 2 y 1.0 and 10 ( –3– – , –1–) 1 4 2 (––, –– ) 14 ( – – , –1– ) – – 2 4 2 – – x 2 28. y = −4sec x ; The graph of y = sec x is 4 2 (–3– –, –1–) vertically stretched by a factor of 4 and reflected about the x-axis. 4 2 1.0 31. y = −2 csc (π x ) ; The graph of y = csc x is horizontally compressed by a factor of 1 , π vertically stretched by a factor of 2, and reflected about the x-axis. y 6 29. y = 4sec ⎛ 1 x ⎞ ; The graph of y = sec x is ( –– , 2) 3 ⎜ 2 ⎟ 2 ⎝ ⎠ horizontally stretched by a factor of 2 and vertically stretched by a factor of 4. y 36 2.0 1.0 1.0 2.0 x 1 –– 3 2 –– 2 6 (0, 4) 32. y = −3sec ⎛ π x ⎞ ; The graph of y = sec x is ⎜ 2 ⎟ 4 2 ( 2 , 4)
62514-0132318806_ISM_02-1.docx