Answer
$y = sec~(\frac{1}{2}x+\frac{\pi}{3})$
We can see the graph below.
Work Step by Step
$y = sec~(\frac{1}{2}x+\frac{\pi}{3})$
When $x = -\frac{5\pi}{3}$, then $y = sec~(-\frac{\pi}{2})~~$(which is undefined)
When $x = -\frac{2\pi}{3}$, then $y = sec~0 = 1$
When $x = \frac{\pi}{3}$, then $y = sec~\frac{\pi}{2}~~$(which is undefined)
When $x = \frac{4\pi}{3}$, then $y = sec~\pi = -1$
When $x = \frac{7\pi}{3}$, then $y = sec~\frac{3\pi}{2}~~$ (which is undefined)
We can see the graph below.