Lesson 2

Lesson 2: Absolute Value Functions

 

Focus

 

Artwork often shows reflections of landscapes and portraits. Many graphic designs also exhibit this type of symmetry. In the case of computer-generated art, it can be quite simple to create a design showing reflective symmetry once one-half of the design is created. Software can be used to duplicate the image and align it to create the desired effect. On the other hand, traditional artwork, such as paintings and sketches, do not provide the artist with the “cut-and-paste” option. Rather, the artist must not only create the same scene twice, but must also pay careful attention to the details of the reflected part to ensure accuracy.

 

In this lesson you will investigate absolute value functions. You will develop techniques to sketch the graphs of absolute value functions based on corresponding linear and quadratic functions. You will discover that you can employ strategies based on reflections in the coordinate plane that will help you to construct the appropriate graphs.

 

Outcomes

 

At the end of this lesson you will be able to

• create a table of values for , given a table of values for

• generalize a rule for writing absolute value functions in piecewise notation

• sketch the graph of ; state the intercepts, domain, and range; and explain the strategy used

Lesson Questions

 

In this lesson you will investigate the following questions:

• How do the properties of compare to those of ?
  
  
• How can absolute value functions be written in piecewise notation?

Assessment

 

Your assessment may be based on a combination of the following tasks:

• completion of the Lesson 2 Assignment (Download the Lesson 2 Assignment and save it in your course folder now.)
  
  
• course folder submissions from Try This and Share activities
  
  
• additions to Module 7 Glossary Terms and Formula Sheet
  
  
• work under Project Connection

Materials and Equipment

 

You will need a graphing calculator and graph paper.