Exponential Modeling and Logarithms

Lesson 9

Math

Unit 5

11th Grade

Lesson 9 of 16

Objective


Describe logarithms as the inverse of exponential functions and graph logarithmic functions.

Common Core Standards


Core Standards

  • F.BF.B.3 — Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
  • F.BF.B.5 — Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
  • F.BF.B.4.B — Verify by composition that one function is the inverse of another.
  • F.BF.B.4.C — Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • F.IF.C.7.E — Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Criteria for Success


  1. Explain that the logarithmic function is the inverse of the exponential function.
  2. Identify the x-intercept and asymptote from the equation of a logarithmic function.
  3. Graph logarithmic functions using either a table of values or properties of inverse functions.
  4. Apply function transformations to logarithmic functions.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

What is $${f^{-1}(x)}$$ when $${f(x)=10^x}$$?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Sketch a graph of the function $${y=\mathrm{log}_3x}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

What transformation do you think would happen with each of these?

$${y=2\mathrm{log}_2x}$$

$${y=\mathrm{log}_2(x-2)}$$

$${y=\mathrm{log}_2(x)+2}$$

 

OR use this Demos activity: Transformations of the Logarithmic Function.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Desmos Transformations of the Logarithmic Function

Transformations of the Logarithmic Function by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed March 22, 2018, 1:18 p.m..

Target Task


The graph of a function $$f$$ is shown below.

a. Sketch the graph of its inverse function $$g$$ on the same axes.

b. Explain how you made your sketch.

References

EngageNY Mathematics Algebra II > Module 3 > Topic C > Lesson 19Exit Ticket, Question #1 and #2

Algebra II > Module 3 > Topic C > Lesson 19 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

icon/arrow/right/large copy

Lesson 8

icon/arrow/right/large

Lesson 10

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Modeling with and Interpreting Exponential Functions

Topic B: Definition and Meaning of Logarithms

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free