Answer
$y = 3~csc~\pi x$
The asymptotes have the form $x = n$, for any integer $n$.
The period is $2$.
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/b18f814f-a38c-45e7-9a4f-fa9d768fae76/result_image/1531722173.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012650Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=1239ff7523da85f696272a7a1ddd53232cf914cff6e2e2c6172844c561081868)
Work Step by Step
$y = 3~csc~\pi x$
When $x = -1$, then $y = 3~csc~(-\pi)~~$ (which is undefined)
When $x = -\frac{1}{2}$, then $y = 3~csc~(-\frac{\pi}{2}) = -3$
When $x = 0$, then $y = 3~csc~0$ (which is undefined)
When $x = \frac{1}{2}$, then $y = 3~csc~\frac{\pi}{2} = 3$
When $x = 1$, then $y = 3~csc~\pi~~$ (which is undefined)
The asymptotes have the form $x = n$, for any integer $n$. The period is $2$.
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/b18f814f-a38c-45e7-9a4f-fa9d768fae76/steps_image/small_1531722173.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012650Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=2b23bcba87be01bdfef3511cb1f98d49d1b817773b0048d2a0cb75e7c662e4e7)