Answer
$$
f(x) = \left\{
\begin{array}{2}
3-x & \quad 0 \leq x \le 3 \\
2x-6 & \quad 3 \lt x \leq 5 \\
\end{array}
\right.
$$
Work Step by Step
The left line has a slope of -1 and a y-intercept of 3, so the equation of the line would be $y=-x+3$.
The slope of the right line is 2 and the line is shifted to the right, from a y-intercept of 0, 3 units. So, the line's equation would be $y=2(x-3)$. Simplified, the equation is $y=2x-6$.
These equations are put into a piecewise function within their domains $[0,3]$ and $(3, 5]$.
