Question

In Problems 39 and 40 , find a function whose graph is given.

Short answer

The function is$y=5\cos \left(\frac{1}{4}x\right)$

Step-by-step solution

Given information

Given the graph

Identify the amplitude

The function takes the form$y=A\cos (\omega x-\varphi )+B$We can see that the period of is $8\pi$therefore we have

$$\begin{gathered} T=\frac{2\mathrm{\pi }}{\omega } \\ 8\pi =\frac{2\pi }{\omega } \\ \omega =\frac{1}{4} \end{gathered}$$

Checking the phase shift and forming the function

On seeing, the phase shift is zero

$$\begin{gathered} A=5 \\ \omega =\frac{1}{4} \\ \varnothing =0 \\ B=0 \end{gathered}$$

So the function is$y=5\cos \left(\frac{1}{4}x\right)$