# Activities

• • • ##### Subject Area

• Math: Algebra II: Logarithms and Exponentials

• ##### Author 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

5.0

## Graph Logarithms

#### Activity Overview

Investigate the graphs of a family of logarithm functions by changing the a-value over the internal 0 to 4.

#### Objectives

For the graphs of f(x)=loga(x) where a>0 and a ≠ 1:

• Infer why the conditions a>0 and a ≠ 1 are necessary for the function to be logarithmic.
• Determine that for z>1 the function is increasing and for 0 Determine the x-intercept, y-intercept, domain, range, and asymptotes
• Determine that for a>1 the function approaches infinity as x approaches infinity and that for 0 < a < 1 the function approaches –infinity as x approaches infinity

#### Vocabulary

• logarithm function
• end behavior
• intercepts
• domain and range
• asymptotes
• increasing and decreasing functions
• extraneous solution