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.

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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.

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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.

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