Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Logarithms and Exponentials

9-12

45 Minutes

• ##### Device
• TI-Nspire™ CX/CX II
• TI-Nspire™ CX CAS/CX II CAS
• TI-Nspire™ Navigator™
• TI-Nspire™
• TI-Nspire™ CAS
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

3.2

## Graphing Exponentials

#### Activity Overview

Investigate the graphs of the family of exponential functions.

#### Objectives

• Infer why the conditions b > 0 and  b ≠ 0 are necessary for the function to be exponential
• Determine that for x > 1 the function is increasing and for 0 < x < 1 the function is decreasing
• Determine that the y-intercept is always (0,1) and there is no x-intercept
• Determine that for b > 1 the function approaches infinity as x approaches infinity and that for 0 < b < 1 the function approaches infinity as x approaches -infinity
• Identify the domain as (-infinity, inifinity) and the range as (0, infinity)
• Identify the equation of the function’s horizontal asymptote as y = 0

#### Vocabulary

• Exponential function
• End behavior
• Intercepts
• Domain and range
• Asymptotes
• Increasing and decreasing functions