Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 22: 68

Answer

Two other everyday examples of step functions include the price of taxi fares as a function of distance travelled and income tax rate as a function of household income.

Work Step by Step

For taxi fares as a function of distance travelled, the fares usually jump once a given distance is travelled. For example, the first four kilometers of a taxi ride might have a fare of \$8, and that fare might increase by \$1 for every kilometer afterwards. The graph of this would be that of a step function. For income tax rate as a function of household income, (for some tax systems) the tax rate stays the same even if your income increases as long as it stays in the same bracket. The tax rate will increase sharply, however, once your income crosses the threshold for the next income bracket. Thus, it could be modeled with a step function.
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