Continuous Functions

Among citizens, taxes are a contentious issue. Every person has their own opinion regarding how much they should be taxed or what parts of their income should be taxed. Above all, people feel that taxes should be fair. Taxes help to fund the various functions we expect from the federal government.

In the United States and many other countries, the tax rate increases as taxable income rises. In many states, a similar state income tax exists. In the state of Arizona (2011), several tax brackets exist for individuals with corresponding tax rates.

This table reflects the progressive side of the tax. The more you make, the higher the tax rate is. However, many people get squeamish when they change income brackets. If your taxable income increased the following year from $9,999 to$10,001, would the change in tax rates lead to a jump in the amount you paid?

In this section, we’ll examine this question in the context of continuous functions. We’ll learn how to recognize a continuous function. This will help us to determine if there are any jumps in the amount a person pays in Arizona when an income increase moves them from one tax bracket to another.

Our objectives for this section are to

• Identify points of discontinuity on a graph.
• Identify points of discontinuity using a limit.

Use the resources below to help you achieve these objectives.

Read in Section 10.5

Section 10.5 Workbook (PDF)

Watch Video Playlist