Lesson 3: Stretches

 

Focus

 

Have you ever been to an amusement park with those crazy mirrors that make you look funny? When the mirror curves inward (is concave), it makes a person look elongated and thinner. The convex mirror bulges outward and results in a short and wide stature. Similar kinds of distortions can take place as you work with transformations.

 

Look at the photos. The lower right photo was distorted to produce the other two. What is similar about the three photos? How could you create either distortion without using a computer? When is it useful to distort a photo in these ways?

In this lesson you will learn to stretch a function horizontally and vertically. You will also learn to relate a graph to the corresponding equation of the form y = af(bx).

 

Lesson Outcomes

 

At the end of this lesson you will be able to

• compare graphs of the form y = af(bx) to the graph y = f(x) and generalize a rule about a and b
  
• sketch a graph of a function of the form y = af(bx) given the graph of y = f(x) and the values of a and b

Lesson Questions

 

You will investigate the following questions:

• How are the graphs of the functions y = f(x) and y = af(bx) related?
• How can you graph the function y = af(bx) given y = f(x)?

Assessment

 

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

• completion of the Lesson 3 Assignment (Download the Lesson 3 Assignment and save it in your course folder now.)
  
• course folder submissions from Try This and Share activities
  
• additions to Glossary Terms and Formula Sheet
  

Materials and Equipment

• graph paper