⎛ ⎞ − csc 1 1 ; The graph of x 39. π ⎛ ⎞ − f f = (0) csc is y x = 2 y ⎜ 3 ⎟ (2 ) (2 ) ⎜ 6 ⎟ tan ⋅π / 6 − tan ⋅ 0 ⎝ ⎠ 0 6 horizontally stretched by a factor of 3, vertically ⎝ ⎠ stretched by a factor of 2, and shifted down 1 unit. = y π π /6 43. 3 − 0 6 3 − π π = /6 = 6 6 3 4 2 2 4 x ( 9– – (3– The average rate of change is . 1) –, π , 1) ( (0 ) (2 ) (2 ⎞ − ⋅ π − sec / 6 sec , f 3– – 8 ⎝ ⎠ = ) 3) ⋅ f 0 π − 0 π /6 ⎛ 6 (9– , 3) – 44. π = 2 −1 = 6 40. π π /6 = ⎛ ⎞ + 3sec 1 1 ; The graph = sec is y x y x 6 of ⎜ 4 ⎟ The average rate of change is . ⎝ ⎠ horizontally stretched by a factor of 4, vertically π stretched by a factor of 3, and shifted up 1 unit. y ( ) ( ) (4 ) = 45. D tan f g x x 8 ( 8 , 5) (0, 5) (8 , 5) 8 8 x ( 4 , 1) (4 , 1) 8 π ⎛ ⎞ ( ) ( ) ( ) = = D 4 tan 4 tan g f x x x (0 ) ( ) ( ) ⎜ ⎟ − f f − 3 0 ⎝ 6 ⎠ π tan / 6 − tan 0 3 /6 41. = = π /6 π = 3 ⋅ 6 = 2 3 π − 0 6 π π 3
39. y = 2 csc ⎛ 1 x ⎞ − 1 ; The graph of y = csc x is f ⎛ π ⎞ − f (0) ⎜ 3 ⎟ ⎜ 6 ⎟ tan (2 ⋅π / 6 ) − tan (2 ⋅ 0 ) ⎝ ⎠ horizontally stretched by a factor of 3, vertically stretched by a factor of 2, and shifted down 1 unit. y 43. ⎝ ⎠ = π − 0 6 π /6 3 − 0 6 3 6 = π /6 = π 6 3 ( 9– – , 1) (3– –, 1) 4 2 2 4 x The average rate of change is . π ( 3– – , 3) (9– – , 3) 8 44. f ⎛ π ⎞ − f (0 ) ⎝ ⎠ = π − 0 6 sec (2 ⋅ π / 6 ) − sec (2 ⋅ 0 ) π /6 = 2 −1 = 6 40. y = 3sec ⎛ 1 x ⎞ + 1 ; The graph of y = sec x is π /6 π 6 ⎜ 4 ⎟ The average rate of change is . ⎝ ⎠ horizontally stretched by a factor of 4, vertically stretched by a factor of 3, and shifted up 1 unit. y 8 π 45. ( f D g ) ( x ) = tan (4 x ) ( 8 , 5) (0, 5) (8 , 5) 8 8 x ( 4 , 1) (4 , 1) 8 ⎛ π ⎞ ( g D f ) ( x ) = 4 ( tan x ) = 4 tan x f ⎜ ⎟ − f (0 ) ( ) ( ) 3 − 0 ⎝ 6 ⎠ tan π / 6 − tan 0 3 41. π − 0 6 = = π /6 = 3 ⋅ 6 = 2 3 π /6 3 π π
62514-0132318806_ISM_02-1.docx