## Precalculus (6th Edition) Blitzer

$$y=\pi \csc \pi x$$
Please note that a cosecant function $y=A\csc Bx$ has range $(- \infty, -|A|] \cup [|A|, \infty )$ and period $\frac{2\pi }{B}$. According to the information given in the question, we find that this is a cosecant function with $|A|=\pi$ and $B=\frac{2\pi }{2 }=\pi$. Thus,$$y=\pi \csc \pi x.$$