Answer
$y=-\frac{1}{2}sin(\frac{3}{2} x)-1$
Work Step by Step
1. Based on the given graph, we can initially identify that it resembles a graph of negative sine shifted 1 unit down.
2. We can determine the amplitude $|A|=\frac{1}{2}$, period $p=\frac{4\pi}{3}$, passing $(0,-1)$.
3. Write a model as $y=-\frac{1}{2}sin(\omega x)-1$
4. We have $\frac{2\pi}{\omega}=\frac{4\pi}{3}$, thus $\omega=\frac{3}{2}$
5. The equation is $y=-\frac{1}{2}sin(\frac{3}{2} x)-1$
