Introduction to

Piecewise FunctionsUnit 8.05

I can write a story based on the graph of a piecewise function. I can create a piecewise function graph based on a story.

Vocabulary• Piecewise Function – A piecewise

function is a function that is defined on a sequence of intervals. (I.e. It takes “pieces” of several functions and combines them, one after the other, into one continuous graph.)

Watch This!

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Watch This!

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For every graph … there is a

story!

• Example: The cat jumps onto the couch, sits a bit, and then jumps up to the shelf to sit for awhile.

This is a Piecewise Function!

• Example: What is the cat doing now?

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Cat is sitting on the shelfJumps down to the floorOn floor for for 3 sec.

Jumps onto a chair

Cat sits on chair awhile.

1

1

3

3

2

2

55

4

4

• Example: Draw a piecewise graph that describes the “rest of the story.”

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The cat is sitting on a chair. He sees a spider on the floor. He jumps down, eats the spider, then walks over and jumps up onto the couch, and then jumps again back up to shelf (her favorite spot to sit and watch the world) and stays there for hours.

Wait!

Vocabulary Interruption!

• Initial Value – In a piecewise function, the initial value is “where the story begins”. It is where time = 0.

Watch out!

An initial value is NOT the same thing as a y-intercept! Why?

Because each “piece” of the function already has it’s own y-intercept! (remember the 4 original graphs!)

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y = 3x + 0y = 3

y = 3x - 12y = 6

• What is the initial value of this piecewise function?

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The cat is sitting on a chair. He sees a spider on the floor. He jumps down, eats the spider, then walks over and jumps up onto the couch, and then jumps again back up to shelf (her favorite spot to sit and watch the world) and stays there for hours.

The cat is sitting on a chair.

Initial Value

• Example: Draw a piecewise graph that describes the “rest of the story.”

Heig

ht

(ft)

Time (sec)

The cat is sitting on a chair. He sees a spider on the floor. He jumps down, eats the spider, then walks over and jumps up onto the couch, and then jumps again back up to shelf (her favorite spot to sit and watch the world) and stays there for hours.

You T

ry It!

• Practice #1: Peter is driving…

Think – Pair – Share!

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Speed (

10 m

ph)

Time (min)

1

1 3

3

22

4

4

Peter drives 25 mph

Get’s on highway (65 mph)Drives on Hwy for 5 minExits highway and comes to a stop at a stop sign.

• Practice #2: Peter is driving… Think – Pair – Share!

Peter reverses out of his driveway then putting his car into drive, accelerates to 35 mph. He drives for 2.5 minutes before arriving at a stoplight. After waiting at the light for 2 min, he again accelerates to 35 mph where he stays for several minutes.

Speed (

10 m

ph)

Time (min)

Part

ner

Pract

ice!

With your partner:

• Take turns reading each paragraph

• Discuss Saundra’s three clients. How are their running styles the same, different?

• Discuss the graphs. How are they the same, different?

• Match each graph with the client it belongs to.

• Together, decide who of the three won the race!

* Raise your hand if you have questions!

You have 15 Seconds to get desks into

tables of 4!

In your groups:

• Make sure everyone is helping

• Come up with a strategy

• Work together to match each graph with its story (1 extra graph! YOU write the story!)

• Copy each graph onto the appropriate space on your guided notes

• Be ready to discuss and defend your decisions/matches

* Raise your hand if you have questions!

 Doobie, Sarah’s c

at was w

alking

along the when he sa

w a bird in

a nearby tree. H

e jumped up

into the tre

e, which fri

ghtened

the bird away. Doobie th

en

jumped down onto the fence

where he continued to walk

hoping the bird would come

back. It didn’t.

Doobie gave up

and jumped to the ground.

 

Jennifer loves to run on her

treadmill at home because she

can monitor her heart rate at

the same time. During one of

her runs she noticed her heart

rate stayed constant during the

first 5 minutes. She then

increased her speed on the

treadmill, which in turn

increased her heart rate. But,

just like her speed, her heart

rate leveled out again as she hit

her stride.

 

Joseph is driving his brand new

Mustang! He heads out of his

driveway and through his

neighborhood. He then takes an

onramp to the freeway. Things

are going well and he is driving

at a constant and safe speed.

All of a sudden he sees an

accident in the road ahead of

him! He slams on his breaks,

stopping just inches from

another car! Joseph and his

Mustang are safe.

When y

ou’r

e d

one…

• As a group, raise your hands and show teacher your completed guided notes

• Be ready to answer an “exit question” from the teacher

• Put your groups desks back where they go

• Get the homework worksheet out and begin working quietly and independently

Homework Time!

Connecting the Pieces WS

I can write a story based on the graph of a piecewise function. I can create a

piecewise function graph based on a story.