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Ch 9: Understanding Function Operations

About This Chapter

Watch online math video lessons and learn about inverse functions, composite functions, one-to-one functions and more. Take the quizzes that follow each lesson to test your knowledge of function operations.

Understanding Function Operations - Chapter Summary and Learning Objectives

You might already be aware of a function's use to calculate input and output values, but if you'd like to learn more about function operations, this chapter can introduce you to some advanced topics. Watch the video lessons to find out what the graph of a one-to-one function looks like and learn how to find the domain and range of a composite function. You can also discover the uses of the horizontal line test to determine which type of function you're dealing with. By the time you finish this chapter, you should be able to:

  • Perform arithmetic operations with functions
  • Graph composite functions
  • Find and graph a function's inverse
  • Identify one-to-one functions
  • Solve equations with multiple variables

Video Objectives
How to Add, Subtract, Multiply, and Divide Functions Find out what's required to perform basic arithmetic operations with functions.
How to Compose Functions Get a refresher on function notation. Learn how to compose a function.
Applying Function Operations Practice Problems Practice composing functions, finding their domain and range and performing arithmetic operations.
Compounding Functions and Graphing Functions of Functions Learn what a composite function is and investigate its graph.
Domain & Range of Composite Functions: Definition & Examples Discover how domain and range are calculated when working with composite functions.
Inverse Functions Find out how to determine the inverse of a function. Explore the uses of the horizontal line test.
Understanding and Graphing the Inverse Function Review steps for finding a function's inverse. Learn how to graph inverse functions.
One-to-One Functions: Definitions and Examples Identify one-to-one functions by examining their graphs and using the horizontal line test.
Manipulating Functions and Solving Equations for Different Variables Explore basic rules for manipulating functions and solving equations with two or more variables.

9 Lessons in Chapter 9: Understanding Function Operations
Test your knowledge with a 30-question chapter practice test
How to Add, Subtract, Multiply and Divide Functions

1. How to Add, Subtract, Multiply and Divide Functions

Combining functions using addition, subtraction, multiplication, and division explains function operations. Discover how to perform function operations using known functions and to define related terminology.

How to Compose Functions

2. How to Compose Functions

Function composition consists of combining two or more functions. Explore how to compose functions, how to evaluate composed functions, and review how to write an equation with function notation.

Applying Function Operations Practice Problems

3. Applying Function Operations Practice Problems

Combining all the properties of functions to solve complex questions is a great way to review and apply function knowledge. Find three practice problems that provide an opportunity to practice solving for function using its domain, range, and inverse functions.

Compounding Functions and Graphing Functions of Functions

4. Compounding Functions and Graphing Functions of Functions

Composite functions are a way of combining functions into one big function by using the output of one function as the input for another. Discover how to evaluate functions from the inside out, compounding functions and graphing functions of functions, as well as what happens to the domain and range of a composite function.

Domain & Range of Composite Functions: Definition & Examples

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.

Inverse Functions

6. Inverse Functions

An inverse function is a function that undoes a previous function. Discover how to find an inverse function and test it graphically using the horizontal line test.

Understanding and Graphing the Inverse Function

7. Understanding and Graphing the Inverse Function

Inverse functions reverse the calculations and output of functions but don't apply to all functions. Follow the five steps of an inverse function and use them to create a graph.

One-to-One Functions: Definitions and Examples

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.

Manipulating Functions and Solving Equations for Different Variables

9. Manipulating Functions and Solving Equations for Different Variables

Manipulating functions in order to solve equations for different variables is possible as long as certain rules are followed. Explore the unknowns of mathematics, how to manipulate functions, examples and rules of manipulation, and how to solve for different variables.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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