Question

A parking garage bases its prices on the number of hours that a vehicle parks in the garage.

Graph of a piecewise function with one piece constant from 0 comma 2 to 2 comma 2 and another piece going from the point 2 comma 2 to 6 comma 10 and another piece going from 6 comma 10 through 7 comma 11 to the right

Based on the graph, what is the pricing scheme the parking garage uses for vehicles?

The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
The first two hours cost $2, between two and four hours cost $1 per hour, and all hours after that cost $0.50.
The first two hours cost $1 per hour, between two hours and six hours cost $2 per hour, and all hours after that cost $1.
The first two hours cost $1 per hour, between two hours and six hours cost $1 per hour, and all hours after that cost $0.50.

Answer 1

The pricing scheme of the function is (a) The first two hours cost $2, between two hours and six hours cost $2 per hour, and all hours after that cost $1.

How to determine the pricing scheme?

The points are given as:

• Constant = (0,2) to (2, 2)
• Another = (2,2) to (6,10)
• Another = (6,10) to (7,11)

The constant interval implies that the first two hours cost $2

Next, we calculate the slope/rate of the other points.

This is done using

m = (y2 - y1)/(x2 - x1)

So, we have:

m1 = (10 - 2)/(6 - 2) = 2

m2 = (11 - 10)/(7 - 6) = 1

This means that:

• The next 4 hours are charged for $2 per hour
• All hours after that cost $1

Hence, the pricing scheme of the function is (a)

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