Answer
$f(x)=\left\{\begin{array}{l}
3~~~~~~~~~~~~\ \mathrm{i}\mathrm{f}~~\ x=2\\
2x-3~~~\ \mathrm{i}\mathrm{f}~~\mathrm{x}\ \neq 2
\end{array}\right.$
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,1)\cup(1,\ \infty)$
Work Step by Step
We see that the graph consists of the line $y=2x-3$, except that there is a jump discontinuity at $x=2$, where the $y$ value becomes $3$. Thus we have:
$f(x)=\left\{\begin{array}{l}
3~~~~~~~~~~~~\ \mathrm{i}\mathrm{f}~~\ x=2\\
2x-3~~~\ \mathrm{i}\mathrm{f}~~\mathrm{x}\ \neq 2
\end{array}\right.$
We see that the domain is all real numbers, and the range is also all real numbers, excluding 1:
Domain: $(-\infty,\ \infty)$
Range: $(-\infty,1)\cup(1,\ \infty)$