1.7 Piecewise Functions 9/20/23

Last updated 5 months ago

17 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

Akwankyerɛ

Intro

Learn It

Practice It: Writing Equations for Piecewise Functions

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

1.7 Piecewise Functions 9/20/23

Last updated 5 months ago

17 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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

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

Akwankyerɛ

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

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

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?

Graph A

Graph B

Graph C

Graph D

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:

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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.

null

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.

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*

null

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

null

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*

null

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:

null

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:

null

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 :)