Characteristics Of Cosecant Graphs

1) Which statement about y = −3csc(x) is true?

Midline is y = −3

Period is π

Reflected across x-axis and vertically stretched by factor 3

Range is [−3, 3]

2) What is the phase shift of y = csc(x + π/3)?

None

Left π/3

Up π/3

Right π/3

3) What is the period of y = csc(x)?

π

2π

π/2

4π

4) What is the midline of y = 3csc(x) - 1?

Y = 0

Y = -1

Y = 1

Y = -3

5) Which statement about y = -csc(x) is true?

Same shape as y = csc(x), period halved

Same shape as y = csc(x), shifted right π

Same shape as y = csc(x), amplitude doubled

Same shape as y = csc(x), reflected across the x-axis

6) The amplitude of y = 5csc(x) is:

1

5

0

Undefined

7) What is the period of y = csc(2x - π)?

2π

π

π/2

4π

8) The vertical asymptotes of y = csc(x − π/4) occur at:

X = π/4 + kπ

X = π/2 + kπ

X = kπ

X = −π/4 + 2kπ

9) What is the range of y = 2csc(x) − 1?

Y ≤ −3 or y ≥ 1

Y ≤ −2 or y ≥ 2

Y ≤ −1 or y ≥ 1

Y ≤ −3 or y ≥ 3

10) The domain of y = csc(x/2) is all real x except:

All real numbers

Multiples of 2π

Odd multiples of π/2

Multiples of π

11) For y = 2csc(x − π/2) + 3, the midline and range are:

Midline y = 3; range y ≤ 1 or y ≥ 5

Midline y = 2; range y ≤ 1 or y ≥ 5

Midline y = 3; range y ≤ −1 or y ≥ 1

Midline y = 0; range y ≤ −2 or y ≥ 2

12) Which statement about intercepts of y = csc(x) is true?

Has y-intercept y = 1

Has no x-intercepts

Has x-intercepts at multiples of π

Has y-intercept y = 0

13) Which function has period π?

Y = csc(x) + π

Y = csc(2x)

Y = csc(x)

Y = csc(x/2)

14) What is the range of y = −csc(x)?

[−1, 1]

(−1, 1)

(−∞, −1) ∪ (1, ∞)

(−∞, −1] ∪ [1, ∞)

15) The vertical asymptotes of y = csc((x − π)/2) occur at:

X = kπ

X = π/2 + kπ

X = π + 2kπ

X = 2kπ

16) What is the period of y = csc(√2 x)?

√2 π

2π√2

π/√2

(π√2)/2

17) Which statement about y = csc(x) + 4 is true?

Midline is y = 4

Period is π

Vertical asymptotes move to x = π/2 + kπ

Graph is shifted right 4

18) The midline of y = -4csc(x) + 2 is: