Answer
$f(x)=\left\{
\begin{array}{cc}
-x-2 & \quad x \leq -2 \\
2 & \quad -2\lt x\lt1 \\
2x-3 & \quad x \geq 1 \\
\end{array}
\right.$
Work Step by Step
Each piece of the function is linear.
When $x\leq-2$, the graph is the line given by
$y=mx+b$ where slope
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{2-1}{-4-(-3)}=-1$ and
y-intercept $b=-2$.
$\implies y=-1(x)+(-2)=-x-2$
When $-2\lt x\lt1$, the graph is the line given by
$y=2$.
When $x\geq 1$, the graph is the line given by $y=mx+b$ where slope
$m=\frac{3-1}{3-2}=2$ and
y-intercept $b=-3$.
$\implies y=2x-3$
So, a piecewise function for the graph is
$f(x)=\left\{
\begin{array}{cc}
-x-2 & \quad x \leq -2 \\
2 & \quad -2\lt x\lt1 \\
2x-3 & \quad x \geq 1 \\
\end{array}
\right.$
