Intro to Piecewise Functions

Introduction to Piecewise functions

Poll

Check in! What is energy level on a scale of 1-10? (1- no energy; 10- all the energy)

• 1-2

• 3-4

• 5-6

• 7-8

• 9-10

This is a piecewise function!

Speed (mph)

​Time (minutes)

​

Multiple Choice

What is most likely being measured?

• Bike speed over time

• Car speed over time

• A child's walking speed over time

There are 3 lines connected.

Speed (mph)

​Time (minutes)

​

b

a

c

Match

What is the bike doing at each of these?

• a

• b

• c

The bike is increasing speed

The bike is maintaining the same speed

The bike is decreasing in speed

• The bike is increasing speed

• The bike is maintaining the same speed

• The bike is decreasing in speed

Think about this scenario

You're a basketball player

A shoe company wants to sponsor you as you play in a tournament.

They will pay you for $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

Math Response

A shoe company wants to sponsor you as you play in a tournament.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

How much will you be paid if you play for 1 minute?

Type answer here

Correct Answer: 50

Deg^°

Rad

Math Response

A shoe company wants to sponsor you as you play in a tournament.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

How much will you be paid if you play for 2 minutes?

Type answer here

Correct Answer: 100

Deg^°

Rad

Math Response

A shoe company wants to sponsor you as you play in a tournament.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

How much will you be paid if you play for 3 minutes?

Type answer here

Correct Answer: 150

Deg^°

Rad

Math Response

A shoe company wants to sponsor you as you play in a tournament.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

How much will you be paid if you play for 4 minutes?

Type answer here

Correct Answer: 400

Deg^°

Rad

Math Response

A shoe company wants to sponsor you as you play in a tournament.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

How much will you be paid if you play for 5.5 minutes?

Type answer here

Correct Answer: 550

Deg^°

Rad

Draw

Create a graph showing the scenario where x represents time in minutes and y represents dollars paid.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

They will pay you $50 per minute if you play for up to 3 minutes. If you play for more than 3 minutes, they will pay you $100 for each minute you play.

Here is the graph on Desmos!

Labelling

Label the pieces of the function.

Drag labels to their correct position on the image

f(x)=100x

f(x)=50x

Open Ended

Why was there a change in slope?

Each piece of the piecewise function has a different equation.

Labelling

Label the equations.

Drag labels to their correct position on the image

y=x-1

y=.75 (x+5)^2 - 6

y=2

Remember that open vs closed circles matter...

Math Response

What is the inequality for this graph? Use "x" as the variable and put it first.

Type answer here

Correct Answer: x>2

Deg^°

Rad

Math Response

What is the inequality for this graph? Use "x" as the variable and put it first.

Type answer here

Correct Answer: x\le2

Deg^°

Rad

Try it with piecewise functions!

Multiple Choice

Multiple Choice

Multiple Choice

Let's have some fun!

Create your own piecewise function on the next page.

Draw

Create a piecewise function of your energy level on a scale of 1-10 over the course of your day.