Answer
$y=cot(\frac{3}{2}x)$
Work Step by Step
Step 1. This graph is similar to the cotangent function $y=cot(kx)$
Step 2. From the given period $\frac{2\pi}{3}$, we have $\frac{\pi}{k}=\frac{2\pi}{3}$, thus $k=\frac{3}{2}$
Step 3. The function is $y=cot(\frac{3}{2}x)$
