Answer
$f(x) =$
\[ \begin{cases}
-2x-2 & -2 \leq x \lt -1 \\
\sqrt {1-x^{2}} & -1\leq x\leq 1 \\
\end{cases}
\]
Work Step by Step
The graphic of the function $-2x-2$ represents the only line that passes through the points (-2,2) and (-1,0) and and the graphic of the function $\sqrt {1-x^{2}}$ represents the top half of the circle with center the origin and radius 1. See the attached figure.
