Q. 39 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the graph 

Step 2: 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

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

Step 3: 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 $y=5\cos \left(\frac{1}{4}x\right)$