Chapter 9, Problem 22CR

To determine

To graph one period of the function and describe the transformation of its previous graph.

Explanation of Solution

Given:

The given function is

  $g(x)=\tan \frac{1}{2}x$

Calculation:

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

The amplitude is $a=1$

And the period is $\frac{2\pi }{b}=\frac{2\pi }{\frac{1}{2}}=4\pi$

Let us plot the graph of one period of the given function-

  

The graph of $g(x)$ is a horizontal stretch by a factor of $2$ and a vertical stretch by a factor of $1$ of the graph of $f\left(x\right)=\tan x$