Chapter 9.5, Problem 7E

To determine

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

Answer to Problem 7E

Solution:- Period = $\frac{\pi }{3}$ .

Explanation of Solution

  $g(x)=\cot 3x$

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

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

  $\begin{array}{l}x=\frac{\pi }{2(3)},-\frac{\pi }{2(3)}\\ x=\frac{\pi }{6},-\frac{\pi }{6}\end{array}$

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