Matching Graphs To Functions

1) Which statement about intercepts is true for y = csc(x − π/3)?

Y-intercept at y = 0

X-intercepts at x = π/3 + kπ

Y-intercept at y = 1

No x-intercepts

2) Which equation has asymptotes at x = π/4 + kπ?

Y = csc(x − π/4)

Y = csc(x/4)

Y = csc(4x)

Y = csc(x + π/4)

3) A cosecant graph has period π and midline y = 0. Which equation fits?

Y = csc(x) + 2

Y = 2csc(x)

Y = csc(x/2) + 2

Y = csc(2x)

4) Which equation corresponds to a cosecant graph shifted down 3 units?

Y = csc(x) - 3

Y = csc(x - 3)

Y = 3csc(x)

Y = csc(3x)

5) Which function has vertical asymptotes at x = kπ and midline y = 0?

Y = csc(x)

Y = sec(x)

Y = cos(x)

Y = tan(x)

6) A graph matches y = -2csc(x). Which statement best describes it?

Period π, midline y = 2

Period 2π, midline y = 0, reflected across x-axis

Period π, midline y = -2

Period 2π, midline y = -2

7) Which equation has period π and midline y = 1?

Y = csc(2x) + 1

Y = csc(x) + 1

Y = csc(x/2) + 1

Y = 2csc(x) + 1

8) What is the range of y = 4csc(x)?

Y ≤ -4 or y ≥ 4

Y ≤ -1 or y ≥ 1

Y ≤ 0 or y ≥ 4

Y ≤ -4 or y ≥ 0

9) Which function has vertical asymptotes at x = π/6 + kπ and midline y = 0?

Y = csc(x + π/6) + 1

Y = csc(x/6)

Y = csc(6x)

Y = csc(x - π/6)

10) Which statement describes y = csc(x) + 5?

Shifted up 5 units; period π

Shifted right 5 units; period π

Shifted up 5 units; period 2π; asymptotes still at x = kπ

Shifted up 5 units; asymptotes move to x = π/2 + kπ

11) Which equation has midline y = −2 and period 2π?

Y = csc(x/2) − 2

Y = csc(2x) − 2

Y = csc(x) − 2

Y = 3csc(x) + 1

12) Which equation has period 3π?

Y = csc(2x/3)

Y = csc(3x)

Y = csc(x)

Y = 3csc(x)

13) Which choice gives the domain of y = csc(2x)?

All real x except x = kπ/2

All real x except x = kπ

All real x except x = kπ/2, k odd

All real x except x = kπ/2, k even

14) Which function is reflected across the x-axis and shifted up 1?

Y = −csc(2x) + 1

Y = csc(x) − 1

Y = −csc(x − 1)

Y = csc(−x) + 1

15) Which function has midline y = 2 and range y ≤ 0 or y ≥ 4?

Y = csc(x) + 2

Y = 4csc(x) + 2

Y = 2csc(x)

Y = 2csc(x) + 2

16) Which equation has vertical asymptotes at x = 2kπ?

Y = csc(2x)

Y = csc(x/2)

Y = csc(x) + 2

Y = csc(x − 2π)

17) Which function has range y ≤ −3 or y ≥ 3?

Y = −csc(x) + 3

Y = csc(3x)

Y = csc(x) + 3

Y = 3csc(x)

18) Which function has period 2π/5 and a downward reflection?

Y = −csc(x/5)

Y = −csc(5x)

Y = csc(5x)

Y = csc(x/5)

19) Which equation has period √2 π?

Y = csc(x/√2)

Y = csc(√2 x)

Y = csc(2x)

Y = √2 csc(x)

20) Which function has midline y = −4 and period π?

Y = csc(2x) − 4

Y = csc(x/2) − 4

Y = −4csc(x)

Y = csc(x) − 4

Matching Graphs to Functions