OBJECTIVES & STANDARDS
Math Objectives
Write equations for piecewise functions
Read the graphs of piecewise functions
Identify whether functions are continuous or discontinuous
Common Core Math Standards
Link to all CCSS Math
Personal Finance Objectives
Represent stepped tax rates using piecewise functions
Use piecewise functions to deepen understanding of marginal and effective tax rates for income or payroll taxes
National Standards for Personal Financial Education
Earning Income
6a: Calculate the amount of taxes a person is likely to pay when given information or data about the person’s sources of income and amount of spending
7a: Investigate the federal and state tax rates applicable to different sources of income
DISTRIBUTION & PLANNING
Distribute to students
OBJECTIVES & STANDARDS
Math Objectives
Write equations for piecewise functions
Read the graphs of piecewise functions
Identify whether functions are continuous or discontinuous
Common Core Math Standards
Link to all CCSS Math
Personal Finance Objectives
Represent stepped tax rates using piecewise functions
Use piecewise functions to deepen understanding of marginal and effective tax rates for income or payroll taxes
National Standards for Personal Financial Education
Earning Income
6a: Calculate the amount of taxes a person is likely to pay when given information or data about the person’s sources of income and amount of spending
7a: Investigate the federal and state tax rates applicable to different sources of income
DISTRIBUTION & PLANNING
Distribute to students
ANALYZE: Which Graph Fits?
Tyrese is a freelance artist who charges a flat fee of $60 for any project that takes 4 hours or less. If a project takes him longer than 4 hours, he charges $15 per hour.
Which of the following graph accurately represents Tyrese’s pricing? How do you know?
Part I: Introducing Piecewise Functions
A piecewise function has multiple “pieces” that follow different rules, depending on the domain (x values).
In your own words, explain why Tyrese’s pricing was a piecewise function.
What other real-life situation(s) might be represented by a piecewise function?
Part II: Writing Equations for Piecewise Functions
We can use case notation to write an equation for piecewise functions. This tells us what rule to apply for each “case” or “piece” of the function.
Here is the equation for Tyrese’s project fees:
