Question 1

Which of the following is the correct period of the tangent function $y = 	an(x)$?

Accepted Answer

$\pi$

Question 2

Given the function $y = a 	an(b(x - c)) + d$, which parameter affects the period of the tangent function?

Accepted Answer

$b$

Question 3

What is the period of the function $y = 	an(2x)$?

Accepted Answer

$\frac{\pi}{2}$

Question 4

Which of the following describes the vertical asymptotes of $y = 	an(x)$?

Accepted Answer

$x = \frac{\pi}{2} + n\pi, \; n \in \mathbb{Z}$

Question 5

If $y = 	an(x - \frac{\pi}{4})$, how is the graph of $y = 	an(x)$ transformed?

Accepted Answer

Shifted right by $\frac{\pi}{4}$ units

Question 6

Which of the following is the correct formula for the period of $y = 	an(bx)$?

Accepted Answer

$\frac{\pi}{b}$

Question 7

A medical device uses the function $y = 3 	an(2x)$ to model a periodic signal. What is the amplitude of this function?

Accepted Answer

Undefined

Question 8

Which of the following is the correct period of the secant function $y = \sec(x)$?

Accepted Answer

$2\pi$

Question 9

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

Accepted Answer

$x = n\pi, \; n \in \mathbb{Z}$

Question 10

A sound engineer is analyzing the function $y = 2 \csc(3x)$ for a repeating signal. What is the period of this function?

Accepted Answer

$\frac{2\pi}{3}$

Question 11

Which transformation occurs to the graph of $y = 	an(x)$ when the equation is changed to $y = -	an(x)$?

Accepted Answer

Reflection across the $x$-axis

Question 12

Which of the following is the correct period of the cotangent function $y = \cot(x)$?

Accepted Answer

$\pi$

Question 13

What are the vertical asymptotes of $y = \cot(x)$?

Accepted Answer

$x = n\pi, \; n \in \mathbb{Z}$

Question 14

A biologist models population cycles using $y = 	an(x) + 2$. What effect does the '+2' have on the graph?

Accepted Answer

Shifts the graph up by 2 units

Question 15

Which of the following is the correct period of the cosecant function $y = \csc(x)$?

Accepted Answer

$2\pi$

Question 16

If $y = 	an(\frac{1}{2}x)$, what is the period of the function?

Accepted Answer

$2\pi$

Question 17

A physicist is studying a wave modeled by $y = 	an(3x - \frac{\pi}{2})$. What is the period of this wave?

Accepted Answer

$\frac{\pi}{3}$

Question 18

Which of the following statements is true about the amplitude of $y = 	an(x)$?

Accepted Answer

The amplitude is undefined

Question 19

Which of the following functions has a period of $2\pi$?

Accepted Answer

$y = \sec(x)$

section 4.5

Study Guide - Practice Questions