Alg1 Lesson 1.18 Piecewise Functions

Lesson 1.18: Piecewise Functions

Obj: I can formulate and evaluate linear piecewise
functions.

EQ: How do I evaluate a piecewise function?

Roles:
Facilitator
Scribe
Resourcer
Includer

Lesson Goals:
● Creative Thinking
● Talk through controversies and conflict
● Recognize and reduce ambiguity
● Encourage thinking based on formulas, vocab,

and prior knowledge

● Help explain ideas to each other
● Own your ideas and work
● Record ideas in your journal
● Answer Questions on Slides
● Follow your team roles

Facilitator

• Make sure that all peers are staying on task.

• Give advice or suggestions to resolve the problem.

• Be sure everyone is able to explain.

Scribe

• Make sure peers organize their results on their own papers.

• Remind peers to use color, arrows, and other math tools to
communicate your mathematics, reasons, and connections.

• Be ready to join the teacher for a huddle.

Resourcer

• Make sure peers are getting the materials needed.

• Make sure that all materials are put away neatly.

• Make sure that peers are logged in to the needed site.

• Help troubleshoot any technology difficulties that may arise.

Includer

• Make sure that all peers are talking about their work.

• Helps keep peers’ voice volume low.

• Encourages everyone to ask questions.

• Communicates conflicts or questions to the teacher.

Poll

How do you plan to contribute to your table?

• Facilitator

• Scribe

• Resourcer

• Includer

Part 1: Piecewise Graphs

Vocabulary

Piecewise Function: a function which is defined not by a single expression
(value), but by two or more. Each expression is valid for some interval in the
domain (condition).

Absolute Value Function: a function that is a piecewise containing two linear
functions with opposite slopes and their point of intersection.
It forms a V shape.

Parts of a Piecewise Graph

Jump: When another piece continues above or below the previous piece

Hole: When a point in a curve or line is not included. It could have a removable point
above or below it.

Horizontal Asymptote: The flat part of an exponential function.

Vertical Asymptote: Something that appears in logarithmic and rational functions
(will see more of this in algebra 2)

Graph of a Piecewise Function with 3 Linear Pieces

​Desmos Link

Random Question of the Day Time

https://wheelofnames.com/4ke-epz We’ll spin the
wheel as a class and spend a minute or so
discussing our answers.

Part 2: Evaluate Piecewise

Functions

Examples

f(x)

Piece to Use

Process

Output

f(0)

1st

¼(0) = 0

0

f(4)

1st

¼(4) = 1

1

f(8)

2nd

2

2

f(14)

2nd

2

2

f(16)

3rd

-(½)16 + 9 = -8 + 9 = 1

1

f(18)

3rd

-(½)18 + 9 = -9 + 9 = 0

0

​Piecewise Graph

Practice

After evaluating each
value, try sketching a
graph of this piecewise
function.

f(x)

Piece to Use

Process

Output

f(0)

f(5)

f(10)

f(12)

f(15)

f(20)

Multiple Choice

What is f(0)?

• 6

• -1

• 5

• Not in the domain.

Multiple Choice

What is f(5)?

• 5

• 4

• -5

• Not in the domain.

Multiple Choice

What is f(10)?

• -5

• 4

• 5

• Not in the domain.

Multiple Choice

What is f(12)?

• -5

• 4

• 5

• Not in the domain.

Multiple Choice

What is f(15)?

• -5

• 4

• 5

• Not in the domain.

Multiple Choice

What is f(20)?

• -5

• 4

• 5

• Not in the domain.

Graph of this Piecewise

Word Cloud

What kind of puzzles do you like to do?

● Go to your calendar paper.

● Select a skill to work on.

● Work on Deltamath.

After finishing these slides...

Poll

How do you feel about today's lesson?

• I can explain it to my table!

• I know it.

• It's becoming familiar..

• I'm not sure how to do this yet...

Open Ended

Submit a picture of your journal for this lesson. Also, give feedback here on how to improve these slides.