csc has vertical asymptotes when x 1 101. 15. = − 2π, − π, 0, π, 2π . − 2π ≤ x x 14. ≤ 2π = y y = tan has vertical asymptotes when y x sin , y x = 3π , x π , π , 3π . 16. 2 2 2 2 x 0 –2π –π π 2π = cot has vertical asymptotes when y x = − − π, π, 2π, 0, 2π . x − –1 graph of y vertically by a factor of 3. 102 105. Answers will vary. – = (– , 3) y 3 – 6 x Section 2.5 ; x = tan is stretched y x 17. 1. = 4 ( x , 3) – – 2. False; depending on the function, there can be any number of vertical asymptotes. 6 18. = −2 = tan ; The graph tan is stretched y x y x π 3. origin; = odd multiples of x of 2 vertically by a factor of 2 and reflected about the = odd multiples of π 4. y-axis; x x-axis. 2 y 4 , 2 – – 5. = cos y x ( ) 6. True 4 = tan is 0. y x 7. The of y-intercept x ( = cot has no 8. y x y-intercept. , 4 2) 4 ; The graph of x The of 9. y-intercept = y 4 19. = sec is 1. y x = cot is stretched cot y x 10. csc has no x y-intercept. vertically by a factor of 4. = y
101. y = sin x , − 2π ≤ x ≤ 2π y 1 14. 15. y = csc x has vertical asymptotes when x = − 2π, − π, 0, π, 2π . y = tan x has vertical asymptotes when x 3π , π , π , 3π –2π –π 0 –1 x π 2π 16. − . 2 2 2 2 y = cot x has vertical asymptotes when x = − 2π, − π, 0, π, 2π . 102 – 105. Answers will vary. Section 2.5 17. y = 3 x ; graph of vertically by a factor of 3. y 6 y = tan x is stretched (– – , 3) x 1. x = 4 ( – – , 3) 2. False; depending on the function, there can be any number of vertical asymptotes. 6 3. origin; x = odd multiples of π 2 18. y = −2 tan x ; The graph of y = tan x is stretched 4. y-axis; x = odd multiples of π 2 vertically by a factor of 2 and reflected about the x-axis. y 5. y = cos x 4 – – , 2 6. True 7. The y-intercept of y = tan x is 0. ( 4 ) x 8. y = cot x has no y-intercept. ( 4 , 2) 4 9. The y-intercept of y = sec x is 1. 19. y = 4 cot x ; The graph of y = cot x is stretched 10. y = csc x has no y-intercept. vertically by a factor of 4.
62514-0132318806_ISM_02-1.docx