Solve each problem. The cost of parking a car at an hourly...

Solve each problem.
The cost of parking a car at an hourly parking lot is 3 dollar for the first half-hour and 2 dollar for each additional half-hour or fraction of a half-hour. Graph the function $f$ that models the cost of parking a car for $x$ hours over the interval $(0,2]$

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Key Concepts

Piecewise Functions

A piecewise function is defined by different expressions over various parts of its domain. In this context, the cost structure is expressed using different constant values over specific half-hour intervals, making the function’s behavior dependent on where the parking time falls within the interval.

Step Functions

A step function is a specific type of piecewise function that maintains constant values over subintervals and jumps to a new value at the endpoints of those intervals. This is relevant for modeling scenarios like parking fees, where additional time segments incur a fixed additional charge regardless of whether the full interval is used.

Graphing of Piecewise/Step Functions

Graphing piecewise or step functions involves plotting horizontal segments for each subinterval of the domain and indicating discontinuities at the boundary points. Typically, open and closed dots are used to showcase whether a point at the boundary is included in the subinterval, which is important in illustrating cost functions that change their rates abruptly.

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