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.

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.) 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! Watch This! Height (ft) Time (sec) Height (ft) Time (sec) Height (ft) Time (sec) Height (ft) Time (sec)

Watch This! Watch This! Height (ft) Time (sec) 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? ___________________ Example: What is the cat doing now? ___________________ ___________________ ___________________ ___________________ ___________________ Height (ft) Time (sec) Cat is sitting on the shelf Jumps down to the floor On floor for for 3 sec. Jumps onto a chair Cat sits on chair awhile

Example: Draw a piecewise graph that describes the “rest of the story.” Example: Draw a piecewise graph that describes the “rest of the story.” Height (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. 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!) 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!)

Vocabulary Interruption! Height (ft) Time (sec) Height (ft) Time (sec) Height (ft) Time (sec) Height (ft) Time (sec) y = 3x + 0 y = 3 y = 3x - 12 y = 6

What is the initial value of this piecewise function? What is the initial value of this piecewise function? Height (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. The cat is sitting on a chair. Initial Value

Example: Draw a piecewise graph that describes the “rest of the story.” Example: Draw a piecewise graph that describes the “rest of the story.” Height (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 Try It!

Practice #1: Peter is driving… Think – Pair – Share! ___________________ Practice #1: Peter is driving… Think – Pair – Share! ___________________ ___________________ ___________________ ___________________ Speed (10 mph) Time (min) Peter drives 25 mph Get’s on highway (65 mph) Drives on Hwy for 5 min Exits highway and comes to a stop at a stop sign.

Practice #2: Peter is driving… Think – Pair – Share! 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 mph) Time (min)

Partner Practice!

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 cat was walking along the when he saw a bird in a nearby tree. He jumped up into the tree, which frightened the bird away. Doobie then 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 you’re done… 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! 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.