Q: Which of the following best describes the domain of the function $$y = \tan x$$?

$$\{x|x \neq \frac{\pi}{2} + k\pi,\ k \text{ is an integer}\}$$

Q: Which of the following describes the domain of $$y = 2 \csc x - 1$$?

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

Q: Which of the following is the correct set of $$x-$$intercepts for $$y = \tan x$$?

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

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

$$\{x|x \neq \frac{\pi}{2} + k\pi,\ k \text{ is an integer}\}$$

Question 1

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

Accepted Answer

$$\{x|x 
eq \frac{\pi}{2} + k\pi,\ k 	ext{ is an integer}\}$$

Question 2

What is the period of the function $$y = 	an x$$?

Accepted Answer

$$\pi$$

Question 3

Which transformation occurs when graphing $$y = 3 \cot(2x)$$ compared to $$y = \cot x$$?

Accepted Answer

Vertical stretch by a factor of 3 and horizontal compression by a factor of $$\frac{1}{2}$$

Question 4

For the function $$y = 2 \csc x - 1$$, what is the range?

Accepted Answer

$$( -\infty, -3 ] \cup [ 1, \infty )$$

Question 5

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

Accepted Answer

It is an odd function with symmetry about the origin.

Question 6

What are the vertical asymptotes of the function $$y = \sec x$$?

Accepted Answer

$$x = \frac{\pi}{2} + k\pi$$, $$k an $$integer

Question 7

A sound engineer is analyzing a signal modeled by $$y = 2 	an(3x). $$What is the period of this function?

Accepted Answer

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

Question 8

Which of the following describes the domain of $$y = 2 \csc x - 1$$?

Accepted Answer

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

Question 9

A medical device uses the function $$y = 	an x to $$model a periodic signal. At which values of $$x in$$ $$[0, 2\pi]$$ does the function have vertical asymptotes?

Accepted Answer

$$x = \frac{\pi}{2}, \frac{3\pi}{2}$$

Question 10

Which of the following is the correct set of $$x-$$intercepts for $$y = 	an x$$?

Accepted Answer

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

Question 11

If $$y = A 	an(\omega x) + B$$, which parameter affects the period of the function?

Accepted Answer

$$\omega$$

Question 12

A physicist models a wave using $$y = 4 \sec(2x). $$What is the period of this function?

Accepted Answer

$$\pi$$

Question 13

Which of the following statements is true about the range of $$y = \cot x$$?

Accepted Answer

The range is $$(-\infty, \infty)$$

Question 14

Which of the following best describes the effect of the transformation $$y = 	an(x) + 2$$?

Accepted Answer

Vertical shift up by 2 units

Question 15

A real-world application uses $$y = 5 \cot(4x). $$What is the period of this function?

Accepted Answer

$$\frac{\pi}{4}$$

Question 16

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

Accepted Answer

$$\{x|x 
eq \frac{\pi}{2} + k\pi,\ k 	ext{ is an integer}\}$$

Question 17

Which of the following is NOT a property of the tangent function?

Accepted Answer

It has vertical asymptotes at integer multiples of $$\pi.$$

Question 18

A signal is modeled by $$y = 2 	an(\frac{1}{2}x). $$What is the period of this function?

Accepted Answer

$$2\pi$$

Question 19

Which of the following best describes the range of $$y = \sec x$$?

Accepted Answer

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

Graphs of Tangent, Cotangent, Cosecant, and Secant Functions

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