Question

graph the following function: $y = \frac{-1}{2} \csc(2x + \pi)$
step 1 of 2: identify the shape of the more basic function that has been shifted, reflected, stretched or compressed.

Explanation:

Step1: Recall basic trig - function

The basic function related to $y = \frac{-1}{2}\csc(2x+\pi)$ is $y = \csc(x)$. The cosecant function $y=\csc(x)=\frac{1}{\sin(x)}$ has vertical asymptotes at $x = n\pi$, where $n\in\mathbb{Z}$, and its graph consists of U - shaped curves between the asymptotes.

Answer:

The basic function is $y = \csc(x)$ which has a shape consisting of U - shaped curves separated by vertical asymptotes at $x=n\pi$, $n\in\mathbb{Z}$.