Math IIIB Performance Task: Piecewise-Defined Functions Question Set 2

A parking garage charges the following amounts for cars parked in the garage:
For the first hour that a car is parked in the garage, there is no charge.
After the first hour, for the next two hours that a car is parked in the garage, there is a $5 charge.
After the third hour, the garage charges $2 for each additional hour that the car is parked in the garage. If a car is parked in the garage for a fraction of an hour, the garage will charge that fraction of the additional hourly rate.

Use the information provided about the parking garage to answer each of the following questions. Refer to the responses you submitted for Question Set 1 for support.

Sketch a graph to model the total cost of parking in the garage over the domain [0, 12]. (10 points)

Write the piecewise-defined function for the total cost of parking in the garage. That is, state the function C(x), where x is the number of hours a car is parked in the garage. (10 points)

The parking garage plans to change the structure of how much it charges for cars that park in it. A graph of the new total cost is shown below. Describe in detail the new structure. (10 points)