Chapter R.4, Problem 83E

Reaction time. While driving a car, you see a child suddenly crossing the street. Your brain registers the emergency and sends a signal to your foot to hit the brake. The car travels a reaction distance D, in feet, during this time, where D is a function of the speed r, in miles per hour that the car is traveling when you see the child. That reaction distance is a linear function given by

$D\left(r\right)=11r+510$.

$D\left(5\right)=6\text{ft},D\left(10\right)=11.5\text{ft},D\left(20\right)=22.5\text{ft},D\left(50\right)=55.5\text{ft},D\left(65\right)=75\text{ft}$

a. Find $D\left(5\right),D\left(10\right),D\left(20\right),D\left(50\right),$ and $\left(D65\right)$.

b. Graph $D\left(r\right)$.

c. What is the domain of the function? Explain.