Answer
$ y $ is continuous on
$$... \cup(-1,3)\cup(3,5) \cup( 5,7) \cup...$$
Work Step by Step
Given $$ y=\tan\frac{\pi x}{2} =\frac{\sin \frac{\pi x}{2}}{\cos \frac{\pi x}{2}}$$
Since the of the denominator is zero at
$\cos \frac{\pi x}{2}=0 \Rightarrow \frac{\pi x}{2}= \frac{\pi }{2}+k\pi \Rightarrow x=2k+1, \ \ k \in Z $
So, $ y $ is continuous on
$$... \cup(-1,3)\cup(3,5) \cup( 5,7) \cup...$$
