# Lesson 2Piece-WiserSolidify Understanding

## Learning Focus

Graph piecewise functions.

Interpret piecewise functions.

Are all piecewise functions continuous?

## 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.

### 5.

Complete the last equation by finding values for and .

### 6.

Sketch a graph of . Label the axes with appropriate units for this context.

### 7.

Compare the equations and . What are the similarities and differences?

### 8.

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

Use the piecewise function to answer the following problems.

### 9.

Sketch the graph of .

### 10.

What is the domain of ?

### 11.

Find:

#### c.

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.

## Retrieval

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

### 3.

Given the quadratic parent function, , create a new function in vertex form, , that fits the description.

### 4.

Shift right and down .

### 5.

Shift left , reflect vertically, and shift up .