About This Chapter
Working with Exponential & Logarithmic Functions - Chapter Summary
High school students need to read and understand a great deal of information both before they graduate and as they move on in college or the professional world. This chapter provides students with focused training on developing their ability to work with exponential and logarithmic functions.
Instead of an endless chapter of information, the chapter has been divided into short, individualized lessons. Students have the option to review all of the lessons in order, but they can also pick and choose lesson topics in which they need the most assistance. The chapter menu provides a list of all lessons available, and since each lesson is only focused on a single topic, students can easily find what they need. After completing this chapter, students will be ready to:
- Understand and describe the transformation of exponential functions
- Define and use the natural base e
- Write inverses of logarithmic functions
- Define and identify basic and shifted graphs of logarithmic functions
- Use the change-of-base formula for logarithms
- Calculate rate and exponential growth as used in the population dynamics problem
- Analyze end behavior of exponential and logarithmic functions
1. Transformation of Exponential Functions: Examples & Summary
A transformation within an exponential function involves different changes to a graph. Explore more about transformations, the basic exponential function, the three types of changes, and examples of each.
2. Using the Natural Base e: Definition & Overview
The natural base e is an irrational number used in calculations and graphing. Learn more about the definition of the natural base e, explore the ways it is used in logarithms and inverse functions, discover how it appears graphically, and apply it to calculating compounds.
3. Writing the Inverse of Logarithmic Functions
Logarithmic functions can be notated in reverse, where the expressions are communicated the same way but are written inversely. Learn this concept through a set of examples, and discover how to solve for the inverse as well.
4. Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples
Logarithmic functions can appear on graphs and be shifted by altering their equation. Learn how graphs can be flipped and shifted, both horizontally and vertically, through the examples provided in this lesson.
5. Using the Change-of-Base Formula for Logarithms: Definition & Example
For logarithms, using the change-of-base formula is essential when trying to calculate a log of a base that is not the standard base 10. Learn more about this formula for logarithms, including the bases, how to use the formula, and an example of it in practice.
6. Calculating Rate and Exponential Growth: The Population Dynamics Problem
Calculating rate and exponential growth is a method that can be used to solve the population dynamics problem. Learn what the population dynamics problem is about, and study the population growth formula and how its also used in other rate problems.
7. Behavior of Exponential and Logarithmic Functions
Exponential and logarithmic functions are the inverse of one another, the variable being in the exponent in the former and serving as the argument in the latter. Discover the definitions and behavior of these related functions.
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Other chapters within the High School Precalculus: Homeschool Curriculum course
- Graphing with Functions Review
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Quadratic Functions Review
- Solving & Graphing Quadratic Functions
- Polynomial Functions Review
- Working with Polynomial Functions
- Graphing Piecewise Functions
- Graph Symmetry
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions & Equations Review
- Graphing Rational Functions
- Exponential & Logarithmic Functions Review
- Trigonometric Functions & Graphs Review
- Solving Trigonometric Identities
- Trigonometric Graphs & Applications
- Understanding Vectors, Matrices & Determinants
- Working with Matrices & Determinants
- Mathematical Sequences & Series Review
- Sets in Algebra
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations
- Precalculus: Homeschool Assignments & Projects
- Homeschool Resources for Precalculus in High School