#### Answer

Refer to the graph below.

#### Work Step by Step

The parent function of $y=-1-2\cos{(5x)}$ is $y=\cos{x}$.
The parent function $y=\cos{x}$ has a period of $2\pi$.
The period of the function $y=\cos{(5x)}$ is $\frac{2\pi}{5}$ so one period of its graph is in the interval $[0, \frac{2\pi}{5}]$
Dividing this interval into four equal parts yield the key x-values $0, \frac{\pi}{10}, \frac{\pi}{5}, \frac{3\pi}{10}$ and $\frac{2\pi}{5}$.
To graph the given function, perform the following steps:
(1) Create a table of values for $y=-1-2\cos{(5x)}$ 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 $[0, \frac{2\pi}{5}]$.
(3) Extend the graph one more period by repeating the cycle in the interval $[\frac{2\pi}{5}, \frac{4\pi}{5}]$.
Refer to the graph in the answer part above.