About This Chapter
How It Works:
- Identify the lessons in the Algebra Connections Functions and Relations chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the algebra topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn about:
- The basics of functions
- The identification and notation of functions
- Domain and range
- Operations with functions
- The composition of functions
- Inverse functions
- Applications of function operations
Algebra Connections is a registered trademark of CPM Educational Program, which is not affiliated with Study.com.
1. What is a Function: Basics and Key Terms
Mapping numbers sounds complex, but we do it when we buy gasoline. We pump gasoline, and the gas station charges us based on the amount of gas that we pump. Learn how this relates to functions while reviewing the basics and notations in this lesson.
2. Functions: Identification, Notation & Practice Problems
A function is simply a rule that takes one number and turns it into another. But some special conditions must apply for it to be a true mathematical function. Learn about those conditions and how we write functions here!
3. Transformations: How to Shift Graphs on a Plane
What is a transformation? Well, it's something that transforms one function into another! To see what I mean and how that looks, check out this lesson!
4. What Is Domain and Range in a Function?
The domain and range are the possible outputs and inputs of a function. In this lesson, learn about what might restrict the domain and how to figure out the domain and range from a graph.
5. 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!
6. 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.
7. 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.
8. 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!
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Other chapters within the Algebra Connections: Online Textbook Help course
- Algebra Connections Chapter 1: Problem Solving
- Algebra Connections Chapter 2: Variables and Proportions
- Algebra Connections Chapter 3: Graphs and Equations
- Algebra Connections Chapter 4: Multiple Representations
- Algebra Connections Chapter 5: Multiplication and Proportions
- Algebra Connections Chapter 6: Systems of Equations
- Algebra Connections Chapter 7: Linear Relationships
- Algebra Connections Chapter 8: Quadratics
- Algebra Connections Chapter 9: Inequalities
- Algebra Connections Chapter 10: Simplifying and Solving
- Algebra Connections Chapter 12: Algebraic Extensions