Question 1

Which trigonometric function is represented by the first graph (red curve) in the images provided?

Accepted Answer

$$\sec(x)$$

Question 2

Which trigonometric function is represented by the second graph (blue curve) in the images provided?

Accepted Answer

$$\csc(x)$$

Question 3

Which trigonometric function is represented by the third graph (green curve) in the images provided?

Accepted Answer

$$	an(x)$$

Question 4

Which trigonometric function is represented by the fourth graph (green curve) in the images provided?

Accepted Answer

$$\cot(x)$$

Question 5

Based on the graphs, which function has vertical asymptotes at $$x = \frac{\pi}{2} + k\pi$$, where $$k is $$any integer?

Accepted Answer

$$	an(x)$$

Question 6

Which function, as shown in the graphs, has a period of $$\pi$$ and passes through the origin?

Accepted Answer

$$	an(x)$$

Question 7

Which function, as shown in the graphs, has vertical asymptotes at $$x = k\pi$$, where $$k is $$any integer, and does not pass through the origin?

Accepted Answer

$$\cot(x)$$

Question 8

Which function, as shown in the graphs, has a period of $$2\pi$$ and vertical asymptotes at $$x = \frac{\pi}{2} + k\pi$$?

Accepted Answer

$$\sec(x)$$

Question 9

Which function, as shown in the graphs, has a period of $$2\pi$$ and vertical asymptotes at $$x = k\pi$$?

Accepted Answer

$$\csc(x)$$

Question 10

Which of the following statements is true about the function shown in the third graph (green curve)?

Accepted Answer

It is undefined at $$x = \frac{\pi}{2}$$ and $$x = -\frac{\pi}{2}.$$

Question 11

Which of the following statements is true about the function shown in the fourth graph (green curve)?

Accepted Answer

It is undefined at $$x = 0$$ and $$x = \pi.$$

Precalculus Study Notes: Trigonometric Functions and Their Properties

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