Lesson plan

# Lesson 17: Logarithmic Functions

teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards HSF-LE.A.4 http://corestandards.org/Math/Content/HSF/LE/A/4
teaches Common Core State Standards HSF-IF.C http://www.corestandards.org/the-standards
teaches Common Core State Standards HSF-IF.C.7.e http://corestandards.org/Math/Content/HSF/IF/C/7/e

# Lesson 17: Logarithmic Functions

This lesson introduces students to logarithmic functions in base 2 and base 10. Building from the work students have done in the previous lessons with logarithms from an exponential point of view, students make sense of logarithmic functions in a familiar context of population growth. They interpret the equations that represent the functions, graph the functions, and consider why the graphs representing logarithmic functions behave a certain way (MP2, MP7).

Students will continue their study of logarithmic functions in a future course, so this lesson is intended as an introduction to them and is closely tied to their work with exponential functions.

Lesson overview

• 17.1 Warm-up: Which One Doesn’t Belong: Functions (5 minutes)
• 17.2 Activity: How Long Will It Take? (20 minutes)
• 17.3 Activity: Another Logarithmic Function (10 minutes)
• Includes "Are you Ready for More?" extension problem
• Lesson Synthesis
• 17.4 Cool-down: Which Graph Represents Which Function? (5 minutes)

Learning goals:

• Create graphs of logarithmic functions and use them to answer questions.
• Describe (orally and in writing) characteristics of logarithmic functions.

Learning goals (student facing):

• Let’s graph log functions.

Learning targets (student facing):

• I can interpret logarithmic functions in context.

Required materials:

• Graphing technology

Required preparation:

• Acquire devices that can run Desmos (recommended) or other graphing technology.
• It is ideal if each student has their own device. (Desmos is available under Math Tools.)

Glossary:

• logarithmic function - A logarithmic function is a constant multiple of a logarithm to some base, so it is a function given by $$f(x) = k \log_{a}(x)$$ where $$k$$ is any number and $$a$$ is a positive number (10, 2, or $$e$$ in this course). The graph of a typical logarithmic function is shown. Although the function grows very slowly, the graph does not have a horizontal asymptote.

• Access the complete Algebra 2 Course glossary.

Standards:

• This lesson builds on the standard: CCSS.HSA-SSE.A.1.aMS.A-SSE.1aMO.A1.SSE.A.1

IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.