Lesson 10: Piecewise Linear Functions
Let’s explore functions built out of linear pieces.
Illustrative Math Unit 8.5, Lesson 10 (printable worksheets)
Lesson 10 Summary
The following diagram shows how to create graphs of non-linear functions with pieces of linear functions.
Lesson 10.1 Notice and Wonder: Lines on Dots
What do you notice? What do you wonder?
Lesson 10.2 Modeling Recycling
- Approximate the percentage recycled each year with a piecewise linear function by drawing between three and five line segments to approximate the graph.
- Find the slope for each piece. What do these slopes tell you?
Lesson 10.3 Dog Bath
Elena filled up the tub and gave her dog a bath. Then she let the water out of the tub.
- 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.
- When did she turn off the water faucet?
- How much water was in the tub when she bathed her dog?
- 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?
Lesson 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.
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?
Lesson 10 Practice Problems
- The graph shows the distance of a car from home as a function of time.
Describe what a person watching the car may be seeing.
- The equation and the graph represent two functions. Use the equation y = 4 and the graph to answer the questions.
When x is 4, is the output of the equation or the graph greater?
What value for x produces the same output in both the graph and the equation?
- This graph shows a trip on a bike trail. The trail has markers every 0.5 km showing the distance from the beginning of the trail.
a. When was the bike rider going the fastest?
b. When was the bike rider going the slowest?
c. During what times was the rider going away from the beginning of the trail?
d. During what times was the rider going back towards the beginning of the trail?
e. During what times did the rider stop?
- The expression -25t + 1250 represents the volume of liquid of a container after t seconds. The expression 50t + 250 represents the volume of liquid of another container after t seconds. What does the equation -25t + 1250 = 50t + 250 mean in this situation?
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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