Answer
Refer to the graph below.
Work Step by Step
The parent function of $y=2-3\cos{x}$ is $y=\cos{x}$.
The parent function $y=\cos{x}$ has a period of $2\pi$ so one period of its graph is in the interval $[0, 2\pi]$.
Dividing this interval into four equal parts yield the key x-values $0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}$ and $2\pi$.
To graph the given function, perform the following steps:
(1) Create a table of values for $y=2-3\cos{x}$ using the key x-values listed above.
(Refer to the table below.)
(2) Plot each point from the table of values and connect them using a sinusoidal curve to complete one period in the interval $[0, 2\pi]$.
(3) Extend the graph one more period by repeating the cycle in the interval $[2\pi, 4\pi]$.
Refer to the graph in the answer part above.
