Education Technology

Graph Logarithms

Published on 08/26/2011

Activity Overview

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


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



  • 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.