Answer
Refer to the graph below.
Work Step by Step
RECALL:
(1) The period of the function $y=\tan{(bx)}$ is $\frac{\pi}{b}$.
(2) The consecutive vertical asymptotes of the function $y=\tan{x}$ are $x=-\frac{\pi}{2}$ and $x=\frac{\pi}{2}$.
Thus, with $b=\frac{1}{4}$, the period of the given function is $\frac{\pi}{\frac{1}{4}}=4\pi$.
Consecutive vertical asymptotes of the given function are $x=-2\pi$ and $2\pi$.
This means that one period of the given function is in the interval $[-2\pi, 2\pi]$.
Dividing this interval into four equal parts give the key x-values: $-\pi, 0, \pi$.
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 aymptotes.
(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.
