#### Answer

Refer to the graph below.

#### Work Step by Step

The parent function of $y=1+\frac{2}{3}\cos{(\frac{1}{2}x)}$ 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 $[0,2\pi]$
Note that the period of $y=d+\cos{(bx)}$ is $\frac{2\pi}{b}$.
The given function has $b=\frac{1}{2}$ so its period is $\frac{2\pi}{\frac{1}{2}}=4\pi$.
This means that one period of the given function is in the interval $[0, 4\pi]$.
Dividing this interval into four equal parts yield the key x-values $0, \pi, 2\pi, 3\pi,$ and $4\pi$.
To graph the given function, perform the following steps:
(1) Create a table of values for $y=1+\frac{2}{3}\cos{(\frac{1}{2}x)}$ 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 $[0,4\pi]$.
(3) Extend the graph one more period by repeating the cycle in the interval $[4\pi, 8\pi]$.
Refer to the graph in the answer part above.