# Lesson 2 Piece-Wiser Solidify Understanding

## Learning Focus

Graph piecewise functions.

Interpret piecewise functions.

Are all piecewise functions continuous?

Technology guidance for today’s lesson:

- Construct a Piecewise Function for a Graph: Casio ClassPad Casio fx-9750GIII

## Open Up the Math: Launch, Explore, Discuss

Rashid is off on another bike ride. He has a route he likes to do on his own and has modeled his ride with the following piecewise function to represent the average number of miles he travels in minutes:

### 1.

What is the domain for this function? What does the domain represent in this context?

### 2.

What is the average rate of change during the interval

### 3.

The average rate of change is greatest in which time interval?

### 4.

Find the value of each and explain what the value means in this context.

#### a.

#### b.

#### c.

### 5.

Complete the last equation by finding values for

### 6.

Sketch a graph of

### 7.

Compare the equations

### 8.

How does point-slope form for linear functions compare to vertex form for quadratic functions?

Use the piecewise function

### 9.

Sketch the graph of

### 10.

What is the domain of

### 11.

Find:

#### a.

#### b.

#### c.

## Ready for More?

Graph the function:

## Takeaways

When finding output values for given input values in a piecewise function, you must:

Piecewise functions and point-slope form:

## Lesson Summary

In this lesson, we graphed piecewise functions and learned that some are discontinuous. We learned how to indicate on a graph whether the point was included in an interval. We also made connections between point-slope form for a line and vertex form for a quadratic function.

Find the solutions for each equation. (There are two solutions.)

### 1.

### 2.

### 3.

Given the quadratic parent function,

### 4.

Shift

### 5.

Shift