1.7 Piecewise Functions 9/20/23

Last updated 10 months ago

17 questions

Note from the author:

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
CCSS.PRACTICE.MP4
CCSS.PRACTICE.MP6
CCSS.HSF.IF.A.2
CCSS.HSF.IF.B.4
CCSS.HSF.IF.B.5
CCSS.HSF.BF.A.1
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
1.7 HFL:  Student Activity Packet
1.7 HFL:  Application Problems

Instructions

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
CCSS.PRACTICE.MP4
CCSS.PRACTICE.MP6
CCSS.HSF.IF.A.2
CCSS.HSF.IF.B.4
CCSS.HSF.IF.B.5
CCSS.HSF.BF.A.1
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
1.7 HFL:  Student Activity Packet
1.7 HFL:  Application Problems

Intro

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.

How much does Tyrese charge for a project that takes him 3 hours?_______ 

How much does Tyrese charge for a project that takes him 8 hours?_______ 

Which of the following graph accurately represents Tyrese’s pricing? How do you know?

Learn It

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:

Tyrese’s business is booming, so he decides to increase his prices. Now, he charges $100 for any project that takes five hours or less. He charges $20 per hour for projects that take longer than 5 hours. Write the new equation for his pricing.


            _______ _______ 
f(x)=
            _______ _______ 

Marshall is renting a bike for the day. It costs $13 for up to one hour. After one hour, the price increases to $20. After three hours, the price increases again to $50. The maximum time he can rent the bike is 10 hours total.

Fill in the blanks to write an equation that represents this situation.

           _______     _______ 
f(x)=   _______     _______ 
           _______     _______ 

What is f(4)?_______ 

What is f(1)?_______ 

For which x values does f(x) = 20?_______ 

What is the domain of this function?_______ 

Practice It: Writing Equations for Piecewise Functions

An airline charges for in-flight internet. It costs $7 for 1 hour or less of internet. It costs $19 for more than 1 hour, with a maximum of 24 hours total.
Equation: * Type in entire inequality for blanks 2 & 4*

          _______       _______ 
f(x)=
          _______       _______ 

Bagels are $1 each if you buy 12 or fewer bagels. If you buy more than 12 bages, they cost $0.75 each.
Equation: type in inequality


     1x                 _______ 
0.75x                _______ 

A parking lot charges $3 to park for anytime up to 2 hours. After 2 hours, they charge $1.50 per hour
Equation: *type in entire inequality for blanks 2 and 4*

          _______         _______ 
f(x)=
          _______        _______ 

Kaustabh is a DJ who charges $200 for any event under 2 hours. For events 2 hours or longer, he charges $100 per hour.
Equation:

          _______      _______ 
f(x)=
          _______      _______ 

Apples cost $3 per pound if you buy less than 5 pounds. If you buy 5 pounds or more, they cost $1.25 per pound.
Equation:

          _______      _______ 
f(x)=
          _______      _______ 

Sara earns $16 per hour working at Foods Co-op. If she works more than 40 hours a week, she earns time-and-a-half (ie. a 50% pay increase) for those overtime hours. Write an equation for her total weekly pay as a function of hours worked.
Equation:
          _______           _______ 
f(x)=
          _______         _______ 

The rest of the assignment is 1.7 Desmos 1, 1.7 Desmos 2. 1.7 Desmos 3, & BONUS 1.7 Desmos 4 :)