Introduction to Piecewise Functions Unit 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.
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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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.