Answer
Refer to the graph below.
Work Step by Step
RECALL:
The graph of the function $y=a\cdot \cos{[b(x-d)]}+c$ is a sinusoidal curve that has:
period = $\frac{2\pi}{b}$
amplitude = $|a|$
phase shift = $|d|$ (to the left when $d\lt0$, to the right when $d\gt0$)
one period is in the interval $[0, 2\pi]$
vertical shift = $|c|$ (upward when $|c|\gt0$, downward when $c\lt0$)
The given function has $a=2, b=3,c=1$ and $d=0$
Thus, the graph of this function has:
period = $\frac{2\pi}{3}$
amplitude = $|2| = 2$
phase shift = 0 (none)
vertical shift = $|1|=1$, upward
One period of this function will be in the interval $[0, \frac{2\pi}{3}]$.
Divide this interval into four equal parts to get the key x-values $0,
\frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2\pi}{3}$.
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) Plot the points from the table of values and connect them using a sinusoidal curve. (Refer to the graph in the answer part above.)
