Answer
$y = tan~(x-\frac{\pi}{2})$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ab9d9949-eee2-4ea9-9874-c004358192d4/result_image/1531671368.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012321Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=4d2e2c11f294a7958b329da0960ad6d0d80c27a28637545040f08cdf21fa41c1)
Work Step by Step
$y = tan~(x-\frac{\pi}{2})$
When $x = 0$, then $y = tan~(-\frac{\pi}{2})~~$ (which is undefined)
When $x = \frac{\pi}{4}$, then $y = tan~(-\frac{\pi}{4}) = -1$
When $x = \frac{\pi}{2}$, then $y = tan~0 = 0$
When $x = \frac{3\pi}{4}$, then $y = tan~\frac{\pi}{4} = 1$
When $x = \pi$, then $y = tan~\frac{\pi}{2}~~$ (which is undefined)
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/ab9d9949-eee2-4ea9-9874-c004358192d4/steps_image/small_1531671368.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012321Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=0f350cd680c61a718973776ce014db8713f890ccf87e6c44f861b67d07e2f647)