Q: Where are the vertical asymptotes of the function $$y = \tan x$$ located?

$$x = (2n+1)\frac{\pi}{2},\ n \text{ is an integer}$$

Q: For the function $$y = \cot x$$, where are the vertical asymptotes located?

$$x = n\pi,\ n \text{ is an integer}$$

Q: Which transformation will shift the graph of $$y = \tan x to $$the right by $$\frac{\pi}{4}$$ units?

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

Q: For the function $$y = \sec x$$, what is the equation for its vertical asymptotes?

$$x = (2n+1)\frac{\pi}{2},\ n \text{ is an integer}$$

Q: Which of the following is the correct domain for $$y = \csc x$$?

$$x \neq n\pi,\ n \text{ is an integer}$$

Q: A sound wave is modeled by $$y = \csc x. At $$which $$x-$$values does the function have vertical asymptotes?

$$x = n\pi,\ n \text{ is an integer}$$

Question 1

Which of the following best describes the period of the function $$y = 	an x$$?

Accepted Answer

$$\pi$$

Question 2

Where are the vertical asymptotes of the function $$y = 	an x$$ located?

Accepted Answer

$$x = (2n+1)\frac{\pi}{2},\ n 	ext{ is an integer}$$

Question 3

Given the function $$y = A 	an(Bx - C) + D$$, what is the formula for the period?

Accepted Answer

$$\frac{\pi}{B}$$

Question 4

Which property is true for both $$y = 	an x$$ and $$y = \cot x$$?

Accepted Answer

Both have a period of $$\pi.$$

Question 5

For the function $$y = \cot x$$, where are the vertical asymptotes located?

Accepted Answer

$$x = n\pi,\ n 	ext{ is an integer}$$

Question 6

Which of the following statements about the graph of $$y = 	an x is $$correct?

Accepted Answer

It is symmetric about the origin.

Question 7

What is the range of the function $$y = \csc x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 8

Which transformation will shift the graph of $$y = 	an x to $$the right by $$\frac{\pi}{4}$$ units?

Accepted Answer

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

Question 9

For the function $$y = \sec x$$, what is the equation for its vertical asymptotes?

Accepted Answer

$$x = (2n+1)\frac{\pi}{2},\ n 	ext{ is an integer}$$

Question 10

Which of the following best describes the symmetry of the secant function $$y = \sec x$$?

Accepted Answer

It is even and symmetric about the y-axis.

Question 11

A medical device uses the function $$y = 2	an(3x - \frac{\pi}{2}) + 1 to $$model a signal. What is the period of this function?

Accepted Answer

$$\frac{\pi}{3}$$

Question 12

Which of the following is the correct domain for $$y = \csc x$$?

Accepted Answer

$$x 
eq n\pi,\ n 	ext{ is an integer}$$

Question 13

If $$y = \cot x is $$used to model a physical process, what is the value of $$y at$$ $$x = \frac{\pi}{2}$$?

Accepted Answer

$$0$$

Question 14

Which of the following statements is true about the graph of $$y = \sec x$$?

Accepted Answer

It has a minimum value of $$1 at$$ $$x = 2n\pi.$$

Question 15

A sound wave is modeled by $$y = \csc x. At $$which $$x-$$values does the function have vertical asymptotes?

Accepted Answer

$$x = n\pi,\ n 	ext{ is an integer}$$

Question 16

Which of the following is the correct range for $$y = \sec x$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 17

Which of the following is NOT a property of the tangent function $$y = 	an x$$?

Accepted Answer

It has vertical asymptotes at $$x = n\pi.$$

Question 18

If $$y = \cot x is $$transformed to $$y = -\cot x$$, what happens to the graph?

Accepted Answer

It is reflected about the x-axis.

Question 19

Which of the following best describes the behavior of $$y = 	an x as$$ $$x$$ approaches $$\frac{\pi}{2}$$ from the left?

Accepted Answer

$$y$$ approaches $$+\infty$$

Question 20

Which of the following is the correct formula for the center point of the principal cycle of $$y = A 	an(Bx - C) + D$$?

Accepted Answer

$$x = \frac{C}{B}$$, $$y = D$$

Graphs and Properties of Tangent, Cotangent, Cosecant, and Secant Functions

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