Graph Trigonometric Functions

Multiple Choice

What is the period of the graph of the function $$y=-2\sec\left(4x\right)+1$$ ?

• $$\frac{\pi}{2}$$

• $$\frac{1}{2}$$

• $$2\pi$$

• $$4$$

Multiple Choice

Which of the following would NOT be labeled on the x-axis of the graph of $$y=-2\sec\left(4x\right)+1$$ ?

• $$\frac{\pi}{8}$$

• $$-\frac{3\pi}{8}$$

• $$\frac{\pi}{6}$$

• $$-\frac{\pi}{2}$$

Multiple Select

Which of the following is an asymptote of the graph of $$y=-2\sec\left(4x\right)+1$$ ? Select all that apply.

• $$x=-\frac{3\pi}{8}$$

• $$x=-\frac{\pi}{4}$$

• $$x=0$$

• $$x=\frac{\pi}{8}$$

Multiple Choice

Which of the following is a minimum of the graph of the function $$y=-2\sec\left(4x\right)+1$$ ?

• $$\left(\frac{3\pi}{8},1\right)$$

• $$\left(\frac{\pi}{4},3\right)$$

• $$\left(0,-1\right)$$

• $$\left(-\frac{\pi}{8},3\right)$$

Multiple Choice

What is the period of the graph of the function $$y=\csc\left(\frac{x}{4}+\frac{\pi}{2}\right)$$ ?

• $$16\pi$$

• $$8\pi$$

• $$\frac{\pi}{2}$$

• $$\frac{\pi}{4}$$

Multiple Choice

Which of the following would NOT be labeled on the x-axis of the graph of $$y=\csc\left(\frac{x}{4}+\frac{\pi}{2}\right)$$ ?

• $$\pi$$

• $$-2\pi$$

• $$2\pi$$

• $$-6\pi$$

Multiple Select

Which of the following is an asymptote of the graph of $$y=\csc\left(\frac{x}{4}+\frac{\pi}{2}\right)$$ ? Select all that apply.

• $$x=-2\pi$$

• $$x=0$$

• $$x=2\pi$$

• $$x=6\pi$$

Multiple Choice

Which of the following is a maximum of the graph of the function $$y=\csc\left(\frac{x}{4}+\frac{\pi}{2}\right)$$ ?

• $$\left(0,1\right)$$

• $$\left(8\pi,1\right)$$

• $$\left(2\pi,-1\right)$$

• $$\left(4\pi,-1\right)$$

Multiple Choice

Which of the following is an asymptote of the graph of $$y=4\cot\left(x+\frac{\pi}{4}\right)$$ ?

• $$x=\frac{\pi}{4}$$

• $$x=-\frac{3\pi}{4}$$

• $$x=\frac{\pi}{2}$$

• $$x=-\frac{\pi}{4}$$

Multiple Select

Where are the zeros (x-intercepts) of the graph of $$y=4\cot\left(x+\frac{\pi}{4}\right)$$ ? Select all that apply.

• $$\left(-\frac{3\pi}{4},0\right)$$

• $$\left(0,0\right)$$

• $$\left(\frac{\pi}{4},0\right)$$

• $$\left(\frac{5\pi}{4},0\right)$$

Fill in the Blanks

Graph the following on a separate sheet of paper: $y=-\cos\left(\frac{\pi x}{3}\right)+2$

Write "ok" in the answer blank to get the question correct, and then check your answer on the next slide.

Fill in the Blanks

Graph the following on a separate sheet of paper: $y=3\csc\left(2x-\frac{\pi}{2}\right)$

Write "ok" in the answer blank to get the question correct, and then check your answer on the next slide.

Fill in the Blanks

Graph the following on a separate sheet of paper: $y=-\frac{1}{2}\tan\left(x-\frac{\pi}{2}\right)-1$

Write "ok" in the answer blank to get the question correct, and then check your answer on the next slide.