The function $$y = \tan(2x) ($$Graph 2)

$$y = \tan(x - \frac{\pi}{4})$$

Question 1

Which of the following functions has a vertical asymptote at $$x = \frac{\pi}{2}$$? Refer to the provided graphs.

Accepted Answer

The function $$y = 	an(2x) ($$Graph 2)

Question 2

Which graph represents the function $$y = 	an(2x)$$?

Accepted Answer

Graph 2

Question 3

Which graph shows vertical asymptotes at $$x = -\pi, 0, \pi$$?

Accepted Answer

Graph 1

Question 4

If the period of $$y = 	an(kx) is$$ $$\pi$$, what is the value of $$k$$?

Accepted Answer

$$k = 1$$

Question 5

Which function has vertical asymptotes at $$x = \pm 2\pi$$?

Accepted Answer

$$y = 	an(\frac{x}{2})$$

Question 6

Which transformation would shift the graph of $$y = 	an(x) to $$have vertical asymptotes at $$x = \frac{\pi}{4}, \frac{3\pi}{4}$$?

Accepted Answer

$$y = 	an(x - \frac{\pi}{4})$$

Question 7

What is the period of the function $$y = 	an(\frac{x}{2})$$?

Accepted Answer

$$2\pi$$

Question 8

Which function has vertical asymptotes at $$x = \pm \frac{\pi}{2}$$?

Accepted Answer

$$y = 	an(2x)$$

Question 9

If the graph of $$y = 	an(x) is $$horizontally compressed by a factor of 2, what is the new period?

Accepted Answer

Question 10

Which function's graph would have vertical asymptotes at $$x = \pm \frac{3\pi}{4}$$?

Accepted Answer

Understanding Vertical Asymptotes of Trigonometric Functions

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