Precalculus: Transformations of Exponential Functions

Objectives

• Students will explore the family of exponential functions of the form f(x) = c*b^x+aand be able to describe the effect of each parameter on the graph of y = f(x)
• Students will be able to determine the equation that corresponds to the graph of an exponential function.
• Students will understand that a horizontal translation and a vertical stretch of the graph of an exponential function are essentially the same.

Vocabulary

• exponential function
• parameter
• translation
• reflection
• vertical shift

About the Lesson

This lesson involves the family of exponential functions of the form f(x) = c*b^x+a 

As a result students will:

• Manipulate sliders, and observe the effect on the graph of the corresponding exponential function.
• Conjecture and draw conclusions about the effect of each parameter on the graph of the exponential function.
• Compare horizontal translation and vertical stretch and manipulate equations to demonstrate they are the same.v
• Match specific exponential functions with their corresponding graphs.