Answer
$y = 2+sin~(2x-\pi)$
We can see the graph below.
The period is $\pi$
The amplitude is $1$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3e19612f-c99a-4e68-94c1-046b38c0d1c9/result_image/1531284336.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020023Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=169f04a88e32eff554cbb11578dbe8137d58cbc2c4c021f8c2a0cf63e3ea5337)
Work Step by Step
$y = 2+sin~(2x-\pi)$
When $x = 0$, then $y = 2+sin~(-\pi) = 2$
When $x = \frac{\pi}{4}$, then $y = 2+sin~(-\frac{\pi}{2}) = 1$
When $x = \frac{\pi}{2}$, then $y = 2+sin~(0)= 2$
When $x = \frac{3\pi}{4}$, then $y = 2+sin~(\frac{\pi}{2}) = 3$
When $x = \pi$, then $y = 2+sin~(\pi) = 2$
We can see the graph below.
The period is $\pi$
The amplitude is $1$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3e19612f-c99a-4e68-94c1-046b38c0d1c9/steps_image/small_1531284336.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T020023Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=c8e5298550f3524f1a588f7b4dad040b2bf93119014bf90cf1f0e264f0052856)