Answer
$$
F(x) = \left\{
\begin{array}{3}
-\$15 x+$600 & \quad 0 \leq x \lt 40 \\
\$0 & \quad 40 \leq x \leq 65 \\
\$15x-$975 & \quad 65 \lt x \leq 100\\
\end{array}
\right.
$$
Work Step by Step
The first equation of the piecewise function can be derived from $y=-15(x-40)$ by observing the slope of the \$15 / mi/hr fee and the graph being shifted to an x-intercept of 40. Expanded out, it is $y= -15x+600$ for the domain $[0,40)$.
The second equation describes the legal driving with no fee (\$0) in the domain $[40,65]$.
The last equation is derived from $y=15(x-65)$ with the fee's slope of 15 and the x-intercept shift of 65. The expansion of this is $y=15x-975$ for domain $(65, 100]$
