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 .