Answer
$f(x)=\left\{
\begin{array}{cc}
-x & \quad x \lt4 \\
-x+1 & \quad x \geq4
\end{array}
\right.$
Work Step by Step
Each piece of the function is linear.
When $x\lt4$, the graph is the line given by
$y=mx+b$ where slope
$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-2-(-3)}{2-3}=-1$ and
y-intercept $b=0$.
$\implies y=-1(x)+0=-x$
When $x\geq 4$, the graph is the line given by
$y=mx+b$ where slope
$m=\frac{-4-(-5)}{5-6}=-1$ and
y-intercept $b=1$.
$\implies y=-x+1$
So, a piecewise function for the graph is
$f(x)=\left\{
\begin{array}{cc}
-x & \quad x \lt4 \\
-x+1 & \quad x \geq4
\end{array}
\right.$
