# Lesson 10

Piecewise Linear Functions

Let’s explore functions built out of linear pieces.

### 10.1: Notice and Wonder: Lines on Dots

What do you notice? What do you wonder?

### 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?

### 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?
4. How long did it take for the tub to drain completely?
5. At what rate did the faucet fill the tub?
6. At what rate did the water drain from the tub?

### 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.

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?