About This Chapter
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
|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.|
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.
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.
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.
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.
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
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.
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.
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
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.
Earning College Credit
Did you know… We have over 220 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Precalculus: High School course
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Graph Symmetry
- Graphing with Functions Review
- Rate of Change
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations