Algebra 2: Exponential vs. Power

by
Texas
Instruments

Published on August 31, 2011

#### Objectives

- For positive values of
*x*, students will identify the following behaviors of exponential and power functions:- For large (
*x*>*a*)*x*-values, exponential functions of the form*y*=*a*^{x}grow faster than power functions of the form =*x*^{a} - For particular
*x*-values, power and exponential functions can be equivalent - On certain intervals, power functions can have greater value than exponential functions

- For large (

#### Vocabulary

- Exponential function
- Power function
- Exponent
- Base

#### About the Lesson

This lesson involves comparing rates of growth between the exponential function *f*(*x*)=*a*^{x} and the power function *g*(*x*)=*x*^{a} for positive *x*-values. As a result, students will:

- Compare the discrete value of these functions for
*a*= 2, 3, 4, and 5 as*x*moves along a number line from 1 to 5. - Compare the graphs of the functions for
*a*= 2, 3, 4, and 5 as*x*moves along the*x*-axis.