Answer
Refer to the graph below.
Work Step by Step
RECALL:
The function $y=a \cdot \cot{(bx)}$ has
(1) a period of $\dfrac{\pi}{|b|}$; and
(2) consecutive vertical asymptotes $x=0$ and $x=\frac{\pi}{|b|}$
The given function has $a=\frac{1}{2}$ and $b=3$.
Thus, the given function has:
period = $\frac{\pi}{3}$
One period of this function is in the interval $[0, \frac{\pi}{3}]$.
Divide this interval into four equal parts to obtain the key x-values $0, \frac{\pi}{12}, \frac{\pi}{6}, \frac{\pi}{4}$.
The consecutive vertical asymptotes of this function are $x=0$ and $x=\frac{\pi}{3}$.
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 listed above.
(3) Plot each point from the table of values then connect them using a smooth curve. (Refer to the graph in the answer part above.)
