# Activities

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• • ##### 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

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Graph Logarithms

Updated on 07/08/2019

#### 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

#### About the Lesson

Students will investigate the graphs of the family of logarithm functions f(x)=loga(x), by changing the a-value over the interval 0 less than or equal to a less than or equal to 4. As a result, students will:

• Infer why the conditions a>0 and a≠1 are necessary.
• Determine how the value of a affects the increasing or decreasing behavior of the function.
• Determine the x-intercept, domain, range, and asymptotes.
• Describe the end behavior.

NOTE: The time varies for this activity depending on whether students create the TI-Nspire document or use the pre-constructed .tns file.