Answer
See the graph below:
Work Step by Step
The two consecutive asymptotes occur at $3x=0\text{ and }3x=\pi $.
By solving $3x=0$, we get
$\begin{align}
& 3x=0\text{ } \\
& x=0\text{ }
\end{align}$
Again, solve $3x=\pi $ to get
$\begin{align}
& 3x=\pi \\
& \text{ }x=\frac{\pi }{3}
\end{align}$
Now, the x-intercept is in between the two consecutive asymptotes.
The x-intercept is given as follows:
$\begin{align}
& x\text{-intercept = }\frac{\left( 0+\frac{\pi }{3} \right)}{2} \\
& =\frac{\left( \frac{\pi }{3} \right)}{2} \\
& =\frac{\pi }{6}
\end{align}$
Thus, the graph passes through $\left( \frac{\pi }{6},0 \right)$ and the x-intercept is $\frac{\pi }{6}$. As the coefficient of the provided cotangent function is $2$ , the points on the graph midway between the x-intercept and the asymptotes have y-coordinates of $2$ and $-2$.
We use the two consecutive asymptotes, $x=0$ and $x=\frac{\pi }{3}$, to graph one full period of $y=2\cot 3x$ from $0\text{ to }\frac{\pi }{3}$.
