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Chapter 1 | Functions and Graphs
Example 1.20 Parking Fees Described by a Piecewise-Defined Function
In a big city, drivers are charged variable rates for parking in a parking garage. They are charged $10 for the first hour or any part of the first hour and an additional $2 for each hour or part thereof up to a maximum of $30 for the day. The parking garage is open from 6 a.m. to 12 midnight. a. Write a piecewise-defined function that describes the cost C to park in the parking garage as a function of hours parked x . b. Sketch a graph of this function C ( x ). Solution a. Since the parking garage is open 18 hours each day, the domain for this function is { x | 0< x ≤18}. The cost to park a car at this parking garage can be described piecewise by the function
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C ( x ) = 10, 0< x ≤1 12, 1< x ≤2 14, 2< x ≤3 16, 3< x ≤4 ⋮ 30, 10< x ≤18 . b. The graph of the function consists of several horizontal line segments.
1.15 The cost of mailing a letter is a function of the weight of the letter. Suppose the cost of mailing a letter is 49¢ for the first ounce and 21¢ for each additional ounce. Write a piecewise-defined function describing the cost C as a function of the weight x for 0< x ≤3, where C is measured in cents and x is measured in ounces.
Transformations of Functions We have seen several cases in which we have added, subtracted, or multiplied constants to form variations of simple
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