Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 9
Math
Unit 5
11th Grade
Lesson 9 of 16
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Lesson Notes
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Describe logarithms as the inverse of exponential functions and graph logarithmic functions.
The core standards covered in this lesson
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
What is $${f^{-1}(x)}$$ when $${f(x)=10^x}$$?
Sketch a graph of the function $${y=\mathrm{log}_3x}$$.
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.
Transformations of the Logarithmic Function by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed March 22, 2018, 1:18 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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..
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.
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Evaluate common and natural logs using tables, graphs, and calculators.
Topic A: Modeling with and Interpreting Exponential Functions
Identify, model, and analyze geometric sequences.
Standards
F.IF.A.3F.IF.B.5F.LE.A.2
Analyze and construct exponential functions that model contexts.
F.IF.B.4F.IF.C.8.BF.LE.A.2
Write and change the form of exponential functions that model compounding interest.
F.BF.A.1.AF.LE.B.5
Define and use $$e$$ in continuous compounding situations.
A.SSE.B.3.CF.BF.A.1.A
Describe the derivation of the formula for the sum of a finite geometric series and use it to solve problems.
A.SSE.B.4
Find the sum of an infinite geometric series.
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Topic B: Definition and Meaning of Logarithms
Describe and evaluate simple numeric logarithms (Part I).
F.LE.A.4
Describe and evaluate simple numeric logarithms (Part II).
F.BF.B.3F.BF.B.4.BF.BF.B.4.CF.BF.B.5F.IF.C.7.E
F.BF.B.4.CF.LE.A.4
Understand and apply the change of base property to evaluate logarithms.
Develop and use the product and quotient properties of logarithms to write equivalent expressions.
Develop and use the power property of logarithms to write equivalent expressions.
F.BF.B.4.BF.LE.A.4
Solve equations with logarithms.
Use logarithms to solve exponential modeling problems (Part I).
A.SSE.A.1.BF.LE.A.4
Use logarithms to solve exponential modeling problems (Part II).
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