- Subject:
- Mathematics
- Material Type:
- Module
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- Ohio Open Ed Collaborative
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# Chapter 6.1 - Exercises

# Chapter 6.1 - Introduction to Exponential and Logarithmic Functions

# Chapter 6.1 - Introduction to Exponential and Logarithmic Functions

# Khan Academy - Exponential Functions

# Khan Academy - Exponential Growth and Decay

# Khan Academy - Graphing Exponential Functions

# Khan Academy - Logarithmic Functions

# Khan Academy - Rules of Exponents

# Paul's Online Notes

# Introduction to Exponential Functions and Logarithm Functions

# Exponential Functions

Exponential and logarithm functions are the basis for the study of growth and decay phenomena such as

- Growth or decay of investment, Compound Interest
- Growth or decay of a population
- Radioactive decay
- Etc.

Both functions are one-to-one and are inverses of each other. First we study exponential functions.

**Review**: Laws of Exponents, domain and range of one-to-one functions and their inverses

**Learning Objectives:**

- Study and understand the basic exponential function
*\(f(x) = b^x, b > 0, b \neq 1\)*- Domain, Range, Intercepts, Asymptote and Graph

- Apply transformations to study general exponential functions
*\(f(x) = a \cdot b^{mx + c} + d\)*- Domain, Range, Intercepts, Asymptote and Graph

- Study and understand the natural exponential function
*\(f(x) = e^x\)* - Solve applications using exponential functions

# Introduction to Logarithmic Functions

A Logarithmic function with base b, where b > 0 and b is not equal to 1, is the inverse of the corresponding exponential function. These functions are useful in the study of computer algorithms and natural growth/decay phenomena of living beings, among other applications.

**Learning Objectives:**

- Study and understand the basic logarithmic function
*\(f(x) = b^x\)*- Domain, Range, Intercepts, Asymptote and Graph

- Study and understand the basic logarithmic function \(a \cdot b^{mx + b} + d\) where
*\(b > 0, b\neq 1\)*- Domain, Range, Intercepts, Asymptote and Graph

- Learn and apply basic properties of logarithms
- \(b^a = c\) if and only if \(log_b(c) =a\)
*\(log_{b} b^x = x\)*for all x and \(b^{log_{b} x} = x \)*for x > 0*