Answer
$f(x)=\begin{cases} -3,\ x\lt 0 \\ \sqrt x,\ x\ge 0\end{cases}$
domain $(-\infty,\infty)$ and range $\{-3\}U[0,\infty)$
Work Step by Step
Step 1. Identify the left line equation as $y=-3$ with $x\lt 0$.
Step 2. Identify the right curve equation as $y=\sqrt x$ with $x\ge 0$.
Step 3. Combine the above to get: $f(x)=\begin{cases} -3,\ x\lt 0 \\ \sqrt x,\ x\ge 0\end{cases}$
Step 4. Identify the domain as $(-\infty,\infty)$ and range as $\{-3\}U[0,\infty)$
