Chapter 9.4, Problem 38E

To determine

To find: The transformation of the graph of $f$ represented by the function $g\left(x\right)$ .

Answer to Problem 38E

The graph of $g$ is a vertical stretch multiplied by factor 3 and followed by the translational $\frac{\pi }{2}$ units right 2 unit to the down of the graph of $f$ .

Explanation of Solution

Given:

The given functions are,

  $\begin{array}{l}f\left(x\right)=\sin x\\ g\left(x\right)=3\sin \left(x+\frac{\pi }{2}\right)-2\end{array}$

Calculation:

Consider the given functions are.

  $\begin{array}{l}f\left(x\right)=\sin x\\ g\left(x\right)=3\sin \left(x+\frac{\pi }{2}\right)-2\end{array}$

Compare the above equation with the general form $g\left(x\right)=2\sin \left(x-h\right)+k$ .

Then,

  $\begin{array}{l}a=3\\ b=1\\ h=-\frac{\pi }{2}\\ k=-2\end{array}$

Thus, the graph of $g$ is a vertical stretch multiplied by factor 3 and followed by the translational $\frac{\pi }{2}$ units right 2 unit to the down of the graph of $f$ .