Chapter 1 - Limits and Their Properties - 1.5 Exercises - Page 88: 25

$f(x)$ has a vertical asymptote at every integer value of $x.$

$f(x)=\csc{\pi x}=\dfrac{1}{\sin{\pi x}}$ Vertical asymptotes occur when the denominator alone is $0\to$ $\sin{\pi x}=0\to \pi x=\pi k\to x=k$ where $k$ is an integer.