About This Chapter
Who's it for?
This unit of our High School Trigonometry Homeschool Curriculum course will benefit any student who is trying to learn about function operations. There is no faster or easier way to learn about function operations. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about composite, inverse and one-to-one functions.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Function Operations unit exam confirm understanding or identify any topics that require review.
Functions Operations Unit Objectives:
- Add, subtract, multiply and divide functions.
- Understand how to compose functions.
- Learn to graph functions of functions.
- Find the domain and range of composite functions.
- Learn how to graph inverse functions.
- Provide examples of one-to-one functions.
- Learn to manipulate functions to solve equations.
- Find out how to solve equations with different variables.
1. How to Add, Subtract, Multiply and Divide Functions
Adding, subtracting, multiplying and dividing functions is about as simple as substituting in expressions and then just doing whichever operation it asks you to do. Check out this video lesson to see some examples of this and learn just how easy it is!
2. How to Compose Functions
Function composition is the process of putting two or more functions together. This video lesson will explain how this process works and also show you how to evaluate functions that have been composed.
3. Applying Function Operations Practice Problems
In this lesson, learn how to apply all the different properties of functions to solve complex problems. From function operations and composition to domain and range, get your practice here!
4. Compounding Functions and Graphing Functions of Functions
We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!
5. Domain & Range of Composite Functions: Definition & Examples
Learn what makes a function a composite function and also learn how the parts of a composite function determine its domain. Also in this video lesson, learn about the range of composite functions.
6. Inverse Functions
Inverse functions are two functions that do exactly opposite things. Check out this lesson to learn about how to write inverse functions, find inverse functions, and predict whether or not they exist.
7. Understanding and Graphing the Inverse Function
If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.
8. One-to-One Functions: Definitions and Examples
Watch this video lesson to learn what makes a one-to-one function different from a regular function. Learn a simple test you can use to check whether a function is one-to-one or not.
9. Manipulating Functions and Solving Equations for Different Variables
Functions can be manipulated to solve for many different variables. There are certain rules to follow, but if the rules are adhered to, solving equations can be quite simple. This lesson will show you how.
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Other chapters within the High School Trigonometry: Homeschool Curriculum course
- Types of Real Numbers: Homeschool Curriculum
- Working with Linear Equations: Homeschool Curriculum
- Graphing Inequalities: Homeschool Curriculum
- Absolute Value Equations: Homeschool Curriculum
- Complex Numbers: Homeschool Curriculum
- Using Systems of Linear Equations: Homeschool Curriculum
- Mathematical Modeling: Homeschool Curriculum
- Introduction to Quadratics: Homeschool Curriculum
- Quadratic Functions: Homeschool Curriculum
- Coordinate Geometry: Homeschool Curriculum
- Functions for Trigonometry: Homeschool Curriculum
- Graph Symmetry: Homeschool Curriculum
- Graphing with Functions: Homeschool Curriculum
- Polynomial Functions Basics: Homeschool Curriculum
- Higher-Degree Polynomial Functions: Homeschool Curriculum
- Difference Quotients: Homeschool Curriculum
- Function Graphs: Homeschool Curriculum
- Exponential Functions: Homeschool Curriculum
- Trigonometric Functions: Homeschool Curriculum
- Triangle Trigonometry: Homeschool Curriculum
- Trigonometric Graphs: Homeschool Curriculum
- Solving Trigonometric Equations: Homeschool Curriculum
- Trigonometric Identities: Homeschool Curriculum
- Trigonometric Applications: Homeschool Curriculum
- Analytic Geometry: Homeschool Curriculum
- Vectors, Matrices & Determinants: Homeschool Curriculum
- Polar Coordinates: Homeschool Curriculum
- Circular Arcs, Circles & Angles: Homeschool Curriculum