Answer
$f(x)=\left\{\begin{array}{l}
-3~~~~\mathrm{i}\mathrm{f}~~x\lt 0\\
\sqrt{x}~~~~\mathrm{i}\mathrm{f}~~x\geq 0
\end{array}\right.$
Domain: $(-\infty,\ \infty)$
Range: $\{-3\}\cup[0,\ \infty$)
Work Step by Step
We see that the graph consists of the horizontal line $y=-3$ from $-\infty$ to 0 and the square root function, $y=\sqrt{x}$ afterwards. Solid circles indicate that the value belongs to that piece of the function (e.g. "$\leq$" or "$\geq$"), while open circles indicate that the value does not (e.g. "$\lt$" or "$\gt$"). Thus we have:
$f(x)=\left\{\begin{array}{l}
-3~~~~\mathrm{i}\mathrm{f}~~x\lt 0\\
\sqrt{x}~~~~\mathrm{i}\mathrm{f}~~x\geq 0
\end{array}\right.$
We see that the domain is all real numbers, while the range is all positive real numbers, including -3 and 0:
Domain: $(-\infty,\ \infty)$
Range: $\{-3\}\cup[0,\ \infty$)
