Answer
$y = 3~sin~\pi x$
We can see the graph below.
The period is $2$
The amplitude is 3
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3731cf65-fb37-48cd-8c29-251e83e707b8/result_image/1531239094.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T014320Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=36af468da4e28ac169485a5e50b584b693c9430e8f6f906eb6eae8b76f6d7157)
Work Step by Step
$y = 3~sin~\pi x$
When $x = 0$, then $y = 3~sin~0 = 0$
When $x = \frac{1}{2}$, then $y = 3~sin~\frac{\pi}{2} = 3$
When $x = 1$, then $y = 3~sin~\pi = 0$
When $x = \frac{3}{2}$, then $y = 3~sin~\frac{3\pi}{2} = -3$
When $x = 2$, then $y = 3~sin~2\pi = 0$
We can see the graph below.
The period is $2$
The amplitude is 3
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3731cf65-fb37-48cd-8c29-251e83e707b8/steps_image/small_1531239094.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T014320Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=ee27a4fa0229a75ea1c22f720c6c16ad55de362f03ede5d77e740bd1111d8fee)