## Introduction to Piecewise-Defined Linear Functions

Some functions come in pieces. In this section, we will learn about how to define and graph functions that are essentially collections of discrete pieces. Examples of something defined this way include designing the profile of a car, figuring out your mobile phone plan, and calculating income tax rates. For example, your tax rate depends on your income and is the same for a range of incomes as shown in the table below:

Marginal Tax Rate Single Taxable Income Married Filing Jointly or Qualified Widow(er) Taxable Income Married Filing Separately Taxable Income Head of Household Taxable Income
10% $0 – 9,275$ $0 – 18,550$ $0 – 9,275$ $0 – 13,250$
15% $9,276 – 37,650$ $18,551 – 75,300$ $9,276 – 37,650$ $13,251 – 50,400$
25% $37,651 – 91,150$ $75,301 – 151,900$ $37,651 – 75,950$ $50,401 – 130,150$
28% $91,151 – 190,150$ $151,901 – 231,450$ $75,951 – 115,725$ $130,151 – 210,800$
33% $190,151 – 413,350$ $231,451 – 413,350$ $115,726 – 206,675$ $210,801 – 413,350$
35% $413,351 – 415,050$ $413,351 – 466,950$ $206,676 – 233,475$ $413,351 – 441,000$
39.6% $415,051+$ $466,951+$ $233,476+$ $441,001+$