Answer
Refer to the graph below.
Work Step by Step
RECALL:
The function $y=c+\cot{x}$ has:
period = $\pi$
vertical shift= $|c|$, (upward when $c \gt0$, downward when $c\lt0$)
consecutive vertical asymptotes: $x=0$ and $x=\pi$
The given function has $c=2$.
Thus, it has:
period = $\pi$
vertical shift = $|2|=2$ (which means that the values of the function vary from $-2$ to $2$
One period of this function is in the interval $[0, \pi]$.
Divide this interval into four equal parts to obtain the key x-values $\frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}$.
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) Plot the points from the table of values and connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
