Lesson 10

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piecewise linear functions

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit 6

Functions and Volume

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10.1 Warm Up - Notice and Wonder: Lines on Dots

What do you notice? What do you wonder?

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Learning Targets

• I can create graphs of non-linear functions with pieces of linear functions.

Success Criteria

Today I am exploring non-linear functions to compute and compare different rates of change.

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10.2 Modeling

Recycling

1. Approximate the percentage recycled each year with a piecewise linear function by drawing between three and five line segments to approximate the graph.
2. Find the slope for each piece. What do these slopes tell you?

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10.3 Dog Bath

Elena filled up the tub and gave her dog a bath. Then she let the water out of the tub.

1. The graph shows the amount of water in the tub, in gallons, as a function of time, in minutes. Add labels to the graph to show this.
2. When did she turn off the water faucet?
3. How much water was in the tub when she bathed her dog?

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10.3 Dog Bath

Elena filled up the tub and gave her dog a bath. Then she let the water out of the tub.

• How long did it take for the tub to drain completely?
• At what rate did the faucet fill the tub?
• At what rate did the water drain from the tub?

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10.4 Distance and Speed

The graph shows the speed of a car as a function of time. Describe what a person watching the car would see.

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Are you ready for more?

The graph models the speed of a car over a function of time during a 3-hour trip. How far did the car go over the course of the trip?

There is a nice way to visualize this quantity in terms of the graph. Can you find it?

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Lesson Summary

A piecewise linear function is a function whose graph is pieced together out of line segments. For different ranges of input, the output is changing at different approximately constant rates so a different line is used for each range.

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10.5 Cool Down: Lin’s Phone Charge

Lin uses an app to graph the charge on her phone.

1. When did she start using her phone?
2. When did she start charging her phone?
3. While she was using her phone, at what rate was Lin’s phone battery dying?

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Reflections

• Can you create graphs of non-linear functions with pieces of linear functions?

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Practice Problems

Must do: All problems

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Lesson Video

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