Answer
Refer to the graph below.
Work Step by Step
RECALL:
(1) The period of the function $y=\cot{(bx)}$ is $\frac{\pi}{b}$.
(2) The consecutive vertical asymptotes of the function $y=\cot{x}$, whose period is $\pi$, are $x=0$ and $x=\pi$.
Thus, with $b=2$, the period of the given function is $\frac{\pi}{2}$.
Consecutive vertical asymptotes of the given function are $x=0$ and $\frac{\pi}{2}$.
This means that one period of the given function is in the interval $[0, \frac{\pi}{2}]$.
Dividing this interval into four equal parts give the key x-values: $\frac{\pi}{8}, \frac{\pi}{4}, \frac{3\pi}{8}$.
To graph the given function, perform the following steps:
(1) Create a table of values for the given function using the key x-values listed above.
(Refer to the attached image table below.)
(2) Graph the consecutive vertical asymptotes.
(3) Plot each point from the table then connect them using a smooth curve, making sure that the curves are asymptotic with the lines in Step (2) above.
Refer to the graph in the answer part above.
