Introduction: Piecewise-Defined Linear Functions
Some functions come in pieces. In this outcome, 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 is 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% | [latex]$0 – $9,275[/latex] | [latex]$0 – $18,550[/latex] | [latex]$0 – $9,275[/latex] | [latex]$0 – $13,250[/latex] |
| 15% | [latex]$9,276 – $37,650[/latex] | [latex]$18,551 – $75,300[/latex] | [latex]$9,276 – $37,650[/latex] | [latex]$13,251 – $50,400[/latex] |
| 25% | [latex]$37,651 – $91,150[/latex] | [latex]$75,301 – $151,900[/latex] | [latex]$37,651 – $75,950[/latex] | [latex]$50,401 – $130,150[/latex] |
| 28% | [latex]$91,151 – $190,150[/latex] | [latex]$151,901 – $231,450[/latex] | [latex]$75,951 – $115,725[/latex] | [latex]$130,151 – $210,800[/latex] |
| 33% | [latex]$190,151 – $413,350[/latex] | [latex]$231,451 – $413,350[/latex] | [latex]$115,726 – $206,675[/latex] | [latex]$210,801 – $413,350[/latex] |
| 35% | [latex]$413,351 – $415,050[/latex] | [latex]$413,351 – $466,950[/latex] | [latex]$206,676 – $233,475[/latex] | [latex]$413,351 – $441,000[/latex] |
| 39.6% | [latex]$415,051+[/latex] | [latex]$466,951+[/latex] | [latex]$233,476+[/latex] | [latex]$441,001+[/latex] |
The topics we will cover in this outcome include:
- Define a piecewise function
- Graph a piecewise function using domain
- Write a piecewise function that represents an application
The learning activities for this outcome include:
- Read: Define and Write Piecewise Functions
- Self-Check: Define and Write Piecewise Functions
- Read: Graph Piecewise Functions
- Self-Check: Graph Piecewise Functions
Licenses & Attributions
CC licensed content, Original
- Outcomes. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Income tax in the United States. Provided by: Wikipedia Located at: https://en.wikipedia.org/wiki/Income_tax_in_the_United_States. License: CC BY-SA: Attribution-ShareAlike.
