Question 1

Which of the following is the correct period for the function $y = -4 	an\left(\frac{1}{4}xight)$?

Accepted Answer

$4\pi$

Question 2

Given the function $y = 	an\left(x + \frac{\pi}{2}ight)$, which transformation has been applied to the parent tangent function?

Accepted Answer

Horizontal shift left by $\frac{\pi}{2}$

Question 3

What is the equation of the reciprocal function for $y = \sin(x)$?

Accepted Answer

$y = \csc(x)$

Question 4

For the function $y = 2\cot\left(\frac{1}{3}x + \frac{\pi}{6}\right)$, what is its period?

Accepted Answer

$3\pi$

Question 5

Which graph transformation occurs for $y = -	an\left(x - \frac{\pi}{2}ight)$ compared to $y = 	an(x)$?

Accepted Answer

Reflection over the $x$-axis and shift right by $\frac{\pi}{2}$

Question 6

If $y = 6\csc\left(\frac{1}{2}x\right)$, what is the amplitude of the function?

Accepted Answer

Undefined

Question 7

Which of the following is the correct equation for a tangent function with a period of $2\pi$ and a vertical shift down by 3 units?

Accepted Answer

$y = 	an(x) - 3$

Question 8

A medical device uses the function $y = -2	an\left(x - \frac{\pi}{2}ight) - 3$ to model sensor output. What is the vertical shift and reflection applied?

Accepted Answer

Shift down 3 units, reflect over $x$-axis

Question 9

Which function has vertical asymptotes at $x = \frac{\pi}{2} + n\pi$, where $n$ is any integer?

Accepted Answer

$y = 	an(x)$

Question 10

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

Question 11

Which of the following is the correct equation for a cotangent function with a period of $\pi$ and a phase shift right by $\frac{\pi}{4}$?

Accepted Answer

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

Question 12

A sound wave is modeled by $y = 2\sec\left(\frac{1}{3}x + \frac{\pi}{6}\right)$. What is the period of this function?

Accepted Answer

$6\pi$

Question 13

Which of the following is the correct reciprocal function for $y = \cos(x)$?

Accepted Answer

$y = \sec(x)$

Question 14

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

Accepted Answer

$2\pi$

Question 15

Which transformation is applied to $y = 	an(x)$ to obtain $y = 	an\left(x + \frac{\pi}{2}ight)$?

Accepted Answer

Shift left by $\frac{\pi}{2}$

Question 16

Which function has vertical asymptotes at $x = n\pi$, where $n$ is any integer?

Accepted Answer

$y = \cot(x)$

Question 17

A chemical reaction is modeled by $y = 6\csc\left(\frac{1}{2}x\right)$. What is the period of this function?

Accepted Answer

$4\pi$

Question 18

Which of the following is the correct equation for a tangent function with a period of $\pi$ and a phase shift left by $\frac{\pi}{3}$?

Accepted Answer

$y = 	an(x + \frac{\pi}{3})$

Question 19

If $y = -2	an\left(x - \frac{\pi}{2}ight) - 3$, what is the amplitude of the function?

Accepted Answer

Undefined

Graphing and Analyzing Tangent, Cotangent, Secant, and Cosecant Functions

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