Chapter 9, Problem 17CR

To determine

To identify the amplitude and period of the function and then graph the function.

Explanation of Solution

Given:

The given function is

  $g(x)=6\sin \pi x$

Calculation:

The given function is of the form $g(x)=a\sin bx$

The amplitude is $a=6$

And the period is $\frac{2\pi }{b}=\frac{2\pi }{\pi }=2$

Let us plot the graph of the given function-

  

The graph of $g(x)$ is a horizontal shrink by a factor of $\frac{1}{\pi }$ and a vertical stretch by a factor of $6$ of the graph of $f\left(x\right)=sinx$