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Algebra IIA Unit IV: Exponential Functions and Logarithms o Foundational Material Perform inverse operations o o o o Goal Study exponential functions and use o Study logarithms, the inverse of exponents o 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 o o o o o Key Vocabulary Asymptote Base Change of Base Formula Common Logarithm Exponential Decay o o o o o o o o o 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 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