#### Answer

Refer to the graph below.

#### Work Step by Step

The given equation is already in the form $y=c+a\cdot \sin{[b(x-d)]}$.
Find one interval of the given function whose length is one period:
\begin{array}{ccccc}
&0 &\le &2\left(x+\frac{\pi}{4}\right)&\le &2\pi
\\&\frac{0}{2}&\le &\frac{2\left(x+\frac{\pi}{4}\right)}{2} &\le &\frac{2\pi}{2}
\\&0 &\le &x+\frac{\pi}{4} &\le &\pi
\\&0-\frac{\pi}{4} &\le &x+\frac{\pi}{4}-\frac{\pi}{4} &\le &\pi-\frac{\pi}{4}
\\&-\frac{\pi}{4} &\le &x &\le &\frac{3\pi}{4}
\end{array}
Thus, one interval of the given function is $[-\frac{\pi}{4}, \frac{3\pi}{4}]$.
Dividing this interval into four equal parts yield the key x-values $-\frac{\pi}{4}, 0, \frac{\pi}{4}, \frac{\pi}{2}, $ and $\frac{3\pi}{4}$.
To graph the given function, perform the following steps:
(1) Create a table of values for the function $y=\frac{1}{2}+\sin{\left(2(x+\frac{\pi}{4})\right)}$ using the key x-values listed above.
(Refer to the table below.)
(2) Plot each point in the table then connect them using a sinusoidal curve.
(Refer to the attached graph in the answer part above.)