Answer
$f(x)=\begin{cases} 2x-3,\ x\lt 2 \\3,\ \ \ \ \ \ \ \ \ \ x=2 \\ 2x-3,\ x\gt 2\end{cases}$
domain $(-\infty,\infty)$ and range $(-\infty,1)U\{ 3\}U(1,\infty)$
Work Step by Step
Step 1. Identify the left line equation as $y=2x-3$ with $x\lt 2$.
Step 2. Identify the right line equation as $y=2x-3$ with $x\gt 2$.
Step 3. Identify the middle point as $y=3$ with $x=2$.
Step 4. Combine the above to get: $f(x)=\begin{cases} 2x-3,\ x\lt 2 \\3,\ \ \ \ \ \ \ \ \ \ x=2 \\ 2x-3,\ x\gt 2\end{cases}$
Step 5. Identify the domain as $(-\infty,\infty)$ and range as $(-\infty,1)U\{ 3\}U(1,\infty)$
