Chapter 9.5, Problem 9E

To determine

To calculate; one period of the function and graph them.

Answer to Problem 9E

Solution:- Period = $4\pi$ .

Explanation of Solution

  $g(x)=3\cot \frac{1}{4}x$

The function is of the form $g(x)=a\cot bx$ where $a=3$ and $b=\frac{1}{4}$ . So, the period is $\frac{\pi }{\left|b\right|}=\frac{\pi }{\frac{1}{4}}=4\pi .$

Asymptotes: $x=\frac{\pi }{2\left|b\right|},-\frac{\pi }{2\left|b\right|}$

  $\begin{array}{l}x=\frac{\pi }{2(\frac{1}{4})},-\frac{\pi }{2(\frac{1}{4})}\\ x=2\pi ,-2\pi \end{array}$

The graph of $g$ is a vertical stretch by a factor of $3$ horizontal stretch by a factor of $4$ of the graph of $f(x)=\cot x.$