Inverses of Exponential Functions
Tom Green
6 min read
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Study Guide Overview
This guide covers the inverse relationship between exponential functions () and logarithmic functions (). It explains their key characteristics, including graphs, asymptotes, and domains/ranges. It also emphasizes the reflection of these functions over the line and how ordered pairs are swapped between inverse functions. Finally, practice questions and exam tips are provided for the AP Pre-Calculus exam.
#AP Pre-Calculus: Inverses of Exponential Functions - Your Night-Before-the-Exam Guide
Hey there! Let's make sure you're feeling awesome about exponential and logarithmic functions for your AP Pre-Calculus exam. This guide is designed to be super clear and helpful, especially when you're doing that last-minute review. Let's get started!
#2.10 Inverses of Exponential Functions
#What's the Big Deal? 🤔
We're diving into logarithmic functions and how they're totally connected to exponential functions. Think of them as two sides of the same coin—or better yet, as inverses of each other! Understanding this relationship is key for the exam. 🔑
#Defining Logarithmic Functions
A logarithmic function looks like this: .
bis the base of the logarithm. It has to be greater than 0 and not equal to 1. *ais the coefficient of the function. It cannot be 0. ### Exponential Functions: A Quick Review
An exponential function is written as: .
ais the coefficient.bis the base.
The magic happens because in exponential functions, the input (x) is the exponent, while in logarithmic functions, the input (x) is the argument of the logarithm. This is why they're inverses! 💡
#The Inverse Relationship
- Exponential Growth: Output values change multiplicatively as input values change additively.
- Logarithmic Growth: Output values change additively as input values change multiplicatively.
Think of it like this: Exponential functions grow super fast, while log...
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