Answer
$f(x)=\left\{\begin{array}{l}
\sqrt[3]{x}~~~\mathrm{i}\mathrm{f}~x\lt 1\\
x+1~~~\mathrm{i}\mathrm{f}~x\geq 1
\end{array}\right.$
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,1)\cup[2,\ \infty$)
Work Step by Step
We see that the graph consists of the cube root function $y=\sqrt[3]{x}$ from $-\infty$ until $x=1$ and the the line $y=x+1$ 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:
$f(x)=\left\{\begin{array}{l}
\sqrt[3]{x}~~~\mathrm{i}\mathrm{f}~x\lt 1\\
x+1~~~\mathrm{i}\mathrm{f}~x\geq 1
\end{array}\right.$
We see that the domain consists of all real numbers, while the range consists of numbers smaller than 1 and greater than or equal to 2:
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,1)\cup[2,\ \infty$)
