Answer
$y = -2+\frac{1}{2}~cos~\frac{\pi}{4}x$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/fa917f4f-a419-4ab9-8024-1cedbe310cca/result_image/1531318776.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021030Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=30ce556f131062383164c9a36e35ec55e13961558d70fedd700c323493d33974)
Work Step by Step
$y = -2+\frac{1}{2}~cos~\frac{\pi}{4}x$
When $x = 0$, then $y = -2+\frac{1}{2}~cos~0 = -1.5$
When $x = 2$, then $y = -2+\frac{1}{2}~cos~(\frac{\pi}{2}) = -2$
When $x = 4$, then $y = -2+\frac{1}{2}~cos~(\pi)= -2.5$
When $x = 6$, then $y = -2+\frac{1}{2}~cos~(\frac{3\pi}{2}) = -2$
When $x = 8$, then $y = -2+\frac{1}{2}~cos~(2\pi) = -1.5$
We can see the graph below.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/fa917f4f-a419-4ab9-8024-1cedbe310cca/steps_image/small_1531318776.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021030Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=61660ec12da3fa904c5fcf79900ed328e14516dff7ac7ae5e34dd69c466d2b8a)