Answer
Refer to the graph below.
Work Step by Step
RECALL:
The function $y=\tan{(bx)}$ has a period of $\frac{\pi}{|b|}$.
The given function has $b=3$.
Thus, it has:
period = $\frac{\pi}{3}$
The consecutive vertical asymptotes of this function are $x=-\frac{\pi}{12}$ and $\frac{\pi}{12}$.
One period of this function is in the interval $[-\frac{\pi}{6}, \frac{\pi}{6}]$.
Divide this interval into four equal parts to obtain the key x-values $-\frac{\pi}{12}, 0, \frac{\pi}{12}$.
To graph the given function, perform the following steps:
(1) Create a table of values using the key x-values listed above. (Refer to the table below.)
(2) Graph the consecutive vertical asymptotes mentioned above.
(3) Plot each point from the table of values then connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
