# Piecewise Functions and Taxes

A terrific example of piecewise functions is our graduated income tax system. In that system, the more you make…the higher percentage you pay. However, you DO NOT pay the higher percentage on all of your income. In the two FAQ’s below,we take a look how all of this works.

This FAQ shows how to take a tax table from the Arizona tax forms and convert it into a piecewise function.

In this FAQ we incorporate the idea that the amount you are taxed depends on the tax bracket you fit in.

This topics comes from Section 1 of Chapter 10 in Applied Calculus and is used in Section 5 of the same chapter.

# Technology Can Be Deceiving…

Suppose you are asked to determine whether a function is discontinuous. Many of you might use technology to help you graph a function to decide what the limits are from the left and right. Remember, a function is continuous at a point if the limits from the left and right are equal and also match the value of the function at the point.

Be aware that the TI calculators, WolframAlpha, and Desmos may give slightly different graphs and lead you to the wrong conclusion.

The new MathFAQ below demonstrates how to graph

in WolframAlpha and Desmos.

Notice how the graphs differ. Which one is the better graph to use if you are deciding if the function is discontinuous?

Goto the MathFAQ >>

# Piecewise Functions and US Postage

Postage on first class mail in the United States is based on weight. Each ounce is charged according to a table published by the US Postal Service. The FAQ below shows how to take this table and write out a piecewise function P(x), where x is the weight of the letter.

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# It’s Tax Time!

I just saw yesterday that the IRS is starting to receive tax returns for the tax year 2016…YIPPEE! In honor of this auspicious moment, I thought I would add a FAQ about how piecewise functions and taxes are related.

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# Make a Table of Values in Google Sheets

Suppose you want to generate a table of values from a formula…perhaps to help evaluate a limit. Google Sheets (or any spreadsheet) can quickly generate the values.

Go to MathFAQ >