analyzing
the first option is not correct since 20 is negative and this would not match the sine function, the graph would be reversed
Second option isnt correct because the amplitude is 1 and the graph will not be as wide as it looks in the graph
The third option has the amplitude because the amplitude is 15+20=35 and on the graph the highest point is 35, now we need to check when x=0 because in the graph when x=0, y=5 so, replace
[tex]\begin{gathered} y=15\sin (\frac{\pi}{4}x+\frac{3\pi}{2})+20 \\ \\ y=15\sin (\frac{\pi}{4}(0)+\frac{3\pi}{2})+20 \\ \\ y=15\sin (\frac{3\pi}{2})+20 \\ \\ y=15(-1)+20 \\ \\ y=-15+20 \\ y=5 \end{gathered}[/tex]
the value is right
then the right option is third
