Answer
Refer to the graph below.
Work Step by Step
RECALL:
The function $y=a \cdot \cos{(bx)}$ has:
amplitude = $|a|$
period = $\frac{2\pi}{b}$
The given function has $a=4$ and $b=\frac{3}{2}$. Thus, the given function has:
amplitude = $|4|=4$
period = $\frac{2\pi}{\frac{3}{2}}=\frac{4\pi}{3}$
This means that one period of the given function is in the interval $[0, \frac{4\pi}{3}]$.
Divide this interval into four equal parts to obtain the key x-values $0, \frac{\pi}{3}, \frac{2\pi}{3}, \pi, \text{ and } \frac{4\pi}{3}$.
To graph the given function, perform the following steps:
(1) Create a table of values substituting each of the key x-values listed above into the given function.
(Refer to the table below.)
(2) Plot each point from the table then connect them using a sinusoidal curve.whose amplitude is $4$.
