Precalculus: Comparing Exponential and Power Functions

Objectives

• Students will be able to use various graphical representations to determine which of two functions is greater for large values of x.
• Students will understand that any exponential function of base greater than 1 will be greater than any power function for sufficiently large values of x.
• Students will be able to determine which of two functions is greater given a graph of the ratio of the two functions.
• Students will be able to construct arguments based on graphs and other reasoning to support the conclusion that exponential functions exceed power functions for sufficiently large values of x.

Vocabulary

• Exponential function
• Power function
• Base

About the Lesson

This lesson provides several different opportunities for students to explore graphical relationships between different exponential and power functions, including an investigation of the ratio of the two functions.