Download Lesson 2: Inverses of Relations and Functions

Algebra IIA
Unit IV: Exponential Functions and Logarithms
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Foundational Material
Perform inverse operations
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Goal
Study exponential functions and use
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Study logarithms, the inverse of exponents
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properties of exponents
and logarithmic functions
Why?
To further build a foundation for higher level mathematics such as statistics and business calculus
These skills can be used to observe, understand, and model relationships in science, social studies and economics
Maximize and minimize area and volume
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Key Vocabulary
Asymptote
Base
Change of Base Formula
Common Logarithm
Exponential Decay
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Exponential Growth
Exponential Equation
Exponential Regression
Inverse Function
Logarithmic Equation
Solve problems and fit data to exponential
and logarithmic models
Logarithmic Function
Logarithmic Regression
Natural Logarithm
Properties of Logarithms
Lesson 2: Inverses of Relations and Functions
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Graph and recognize inverses of relations and functions
Find inverses of functions
Read values of an inverse function from a graph or a table, given that the function has an inverse. (CC.9-12.F.BF.4c)
Graphing Inverse Functions:
What is the additive inverse of 3? _________ What is the multiplicative inverse of 5? ___________
Just as there are inverse operations for numbers, we can apply inverse operations to relations and functions by simply
reflecting the points across the line 𝑦 = 𝑥.
Growth Example:
Decay Example:
1𝑥
𝑦 = 3𝑥
𝑦=4
x
-2 -1 0 1 2 3
x
-2 -1 0 1 2 3
𝑥
𝑦=3
1𝑥
𝑦=4
f ( x ) Table: (x,y)
x
y
f -1 ( x ) Table: (y,x)
y
x
f ( x ) Table: (x,y)
x
y
f -1 ( x ) Table: (y,x)
y
x
Writing Inverse Functions: For the functions that follow, write the inverse.
Steps:
f ( x) =
x
3
f ( x) =
x
-5
4
f ( x ) = 3( x - 7)
A clerk needs to price a digital camera returned by a customer. The customer paid a total of $103.14, which included
a gift-wrapping charge of $3.00 and then 8% sales tax. What price should the clerk mark on the tag?
Step 1: Write cost function.
Step 2: Find the inverse of the cost function.
Step 3: Evaluate the inverse function for c = $103.14
Classwork: Worksheet
Assignment: Page 245, 19-27 odd, 33, 49