The cost of parking a car at an airport hourly parking lot...

The cost of parking a car at an airport hourly parking lot is 3 dollars for the first half-hour and 2 dollars for each additional half-hour or fraction thereof. Graph the function defined by $y=f(x)=$ the cost of parking a car for $x$ hours. Use the interval $(0,2]$.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Domain and Interval Analysis

Identifying the correct domain and subintervals is crucial when working with piecewise functions. For the parking cost scenario, the interval (0,2] is divided into segments corresponding to each half-hour, with each segment having a specific cost associated with it.

Rounding Up (Ceiling Concept)

The phrase 'or fraction thereof' implies that any partial half-hour is charged as a full half-hour. This requires using a rounding mechanism similar to the ceiling function, which rounds a number up to the nearest integer. This concept ensures that even if a car is parked for a fraction of a half-hour beyond the first half-hour, it is charged as a full unit.

Piecewise Functions

These are functions defined by different expressions over different intervals of the domain. In the context of the parking cost problem, the rate changes after the first half-hour, so the function that describes the cost is defined by one rule for the first half-hour and another rule for each subsequent half-hour period.

Step Functions

Step functions remain constant over specific intervals and jump at certain points. The parking cost function is a step function because the cost is fixed within each half-hour interval and then jumps to a higher cost at the boundary of the next half-hour due to the 'or fraction thereof' clause.

Transcript

Please give Ace some feedback