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
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 15 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 xintercept 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 xintercept, 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 yaxis 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.