Answer
$$y=\sec \frac{3}{4}x$$
Work Step by Step
Please note that a secant function $y=A\sec Bx$ has range $(- \infty, -|A|] \cup [|A|, \infty )$ and period $\frac{2\pi }{B}$.
Looking at the graph, we find that it can be the graph of a secant function with $|A|$=1 and $B=\frac{2\pi }{\frac{8\pi }{3}}=\frac{3}{4}$. Thus,$$y=\sec \frac{3}{4}x.$$
