Answer
$$
f(x)= \left\{
\begin{array}{3}
-\frac{3}{2} x - 3 & \quad -4 \le x \le -2 \\
\sqrt{4 - x^2} & \quad -2 \lt x \lt 2 \\
\frac{3}{2} x- 3 & \quad 2 \le x \le 4 \\
\end{array}
\right.
$$
Work Step by Step
One will notice that the graph appears to be an absolute value function split into 2 by a semi circle. The absolute value function has a slope of $-\frac{3}{2} $ and $+\frac{3}{2} $ and a y-intercept of $-3$. So the equation of this line is $y = \pm \frac{3}{2} x \ -3$.
The semi circle has a radius of $2$ and a center at $(0, \ 0)$. Therefore, its equation would be $y= \sqrt{4 - x^2}$. This equation's domain is $(-2, 2)$.
