Graphs of Logarithmic Functions  (Lesson 3.5)

Unit 3 - Day 6

​Learning Objectives​
  • Sketch logarithmic functions using the key points (1,0) and (b,1)

  • Connect key features (domain, range, asymptotes, and end behavior) on the graphs of exponential and logarithmic functions

  • Describe transformations of an logarithmic function and graph using the key points (1, 0) and (b, 1

Quick Lesson Plan
Activity: Lumberjack Graphs



Lesson Handout

Answer Key

Experience First

This lesson introduces graphing logarithms, which are the inverses of exponential functions.  In yesterday’s lesson, we formalized what a logarithm is and showed how to get it from an exponential function  Students should work through Questions 1-5 in groups to explore graphs of logarithms. They start by exploring the graph of a log with base 2, where they’ll identity the domain, range, and see the vertical asymptote at x = 0.


In Question 4, we want them to see how the base of a log affects the steepness of the curve, just like with exponential functions, but does not change the x-intercept or vertical asymptote. They will then use their knowledge of transformations to identify the changes in a graph that has been transformed 3 units to the right.

Formalize Later

Remind the students of the connection between logarithms and exponential functions.  In Question 4, emphasize that all logarithmic functions go through the point (1, 0) because the log(1) = 0 and through the “base point,” or (b, 1).  They will see that transformations affect the x-intercept, asymptote, and domain, but not the range.  In fact, no transformations will affect the range since it is always all real numbers.

Students will see a reflection across the y-axis in the Check Your Understanding that will affect the domain, but keep the vertical asymptote the same.  Emphasize that you cannot evaluate the log or 0 or a negative number.