Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of the function $y=c+a\cdot \sin{(bx)}$ is a sinusoidal curve that has:
period = $\frac{2\pi}{b}$
amplitude = $|a|$
one period is in the interval $[0, \frac{2\pi}{b}]$
vertical shift = $|c|$ (upward when $c\gt0$ and downward when $c\lt0$)
The given function has $a=-3, b=2,$ and $c=-1$.
Thus, the graph of this function has:
period = $\frac{2\pi}{2}=\pi$
amplitude = $|-3| = 3$
vertical shift = $|-1|=1$, downward
Since $a$ is negative, the graph also involves a reflection about the x-axis of the parent function.
One period of this function will be in the interval $[0, \pi]$.
Divide this interval into four equal parts to get the key x-values $0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi$.
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.)
