Remediation Unit 2 Lessons 3 - 4 (Graphing Trig)

Unit 2 Lessons 3 - 4 (Graphing Trig)

Graphing csc and sec graphs

Multiple Choice

Which is an asymptote for

$$y=-2\csc\left(\frac{x}{3}+\frac{\pi}{2}\right)-1$$  ?

• $$\frac{3\pi}{4}$$  

• $$\frac{3\pi}{2}$$  

• $$3\pi$$  

• $$-\frac{9\pi}{4}$$  

Multiple Choice

What is the period of the graph of 

 $y=-3\sec\left(2x-\pi\right)+1$  ?

•  $\frac{\pi}{2}$  

•  $\frac{2\pi}{3}$  

•  $\pi$  

•  $\frac{\pi}{3}$  

Multiple Choice

Which is NOT an asymptote of  $y=-3\sec\left(2x-\pi\right)+1$  ?

• $\frac{\pi}{2}$

• $\frac{3\pi}{4}$

• $\frac{5\pi}{4}$

• $\frac{7\pi}{4}$

Multiple Choice

What is the ending point in the table for

 $y=-3\sec\left(2x-\pi\right)+1$  ?

•  $\left(6\pi,\ 0\right)$  

•  $\left(\frac{\pi}{2},\ 2\right)$  

•  $\left(\frac{3\pi}{2},\ 0\right)$  

•  $\left(\frac{3\pi}{2},\ -2\right)$  

Multiple Choice

What is the period of

 $y=-\frac{1}{2}\cot\left(\frac{x}{3}-\pi\right)+4$  ?

•  $\frac{\pi}{3}$  

•  $3\pi$  

•  $\frac{2\pi}{3}$  

•  $6\pi$  

Multiple Choice

What is the beginning x value in the table for the function

 $y=\frac{1}{2}\tan\left(\frac{x}{2}-\frac{\pi}{3}\right)-1$  ?

•  $-\frac{\pi}{3}$  

•  $\frac{2\pi}{3}$  

•  $-\frac{2\pi}{3}$  

•  $-\frac{2\pi}{5}$  

Multiple Choice

What is the distance between each point (the "add number") in the table for

 $y=2\tan\left(2x+\frac{\pi}{3}\right)-2$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{8}$  

•  $\pi$  

•  $\frac{2\pi}{3}$  

Multiple Choice

Which number will affect the amplitude of the graph of

 $y=-2\csc\left(\frac{x}{3}+\frac{\pi}{2}\right)-1$  ?

•  $-2$  

•  $3$  

•  $2$  

•  $-1$  

Multiple Choice

Which is an asymptote for

 $y=-2\csc\left(\frac{x}{3}+\frac{\pi}{2}\right)-1$  ?

•  $-\frac{3\pi}{4}$  

•  $3\pi$  

•  $\frac{3\pi}{2}$  

•  $\frac{3\pi}{4}$  

Graphing tan and cot graphs

Multiple Choice

Find the period of

 $y=2\tan\left(2x+2\pi\right)$  .

•  $2\pi$  

•  $\pi$  

•  $\frac{\pi}{2}$  

•  $4\pi$  

Multiple Choice

Which is an asymptote for

 $y=-\frac{1}{2}\cot\left(\frac{x}{3}-\pi\right)+4$  ?

•  $9\pi$  

•  $\frac{15\pi}{4}$  

•  $\frac{9\pi}{2}$  

•  $\frac{21\pi}{4}$  

Multiple Choice

Which is a point on the graph of

 $y=-\frac{1}{2}\cot\left(\frac{x}{3}-\pi\right)+4$  ?

•  $\left(\frac{21\pi}{4},\ 3\frac{1}{2}\right)$  

•  $\left(3\pi,\ 4\right)$  

•  $\left(\frac{15\pi}{4},\ 4\frac{1}{2}\right)$  

•  $\left(\frac{9\pi}{2},\ 4\right)$  

Multiple Select

Check all transformations that apply to the function:

 $y=-2\cot\left(2x+2\pi\right)-2$  

• horizontal stretch

• vertical stretch

• shift left

• shift up

• reflects y-axis