Ch 9: Properties of Functions

About This Chapter

Watch math video lessons and learn all about functions, including function notations, transformations and more. These video lessons are short and engaging and make learning easy!

Properties of Functions - Chapter Summary and Learning Objectives

What are functions and why do you need to know about them? Is it essential to use function notation in mathematical equations? Why is this concept so important? If you are feeling overwhelmed with questions about the properties of functions, then take a deep breath, relax and watch our lessons. They will demystify this whole concept for you. To help calm your nerves before you watch the video lessons, we'll point out that a function is actually a pretty easy concept to understand.

As you start to work more with functions, you will see a need to learn how to add, subtract, multiply and divide them, so we offer lessons covering all that. You also will need to know how to compose functions, so check out our videos on this topic.

Working with functions, you're going to need to have an understanding of values that are simply not allowed in a function. Find out what a zero denominator and negative root have in common and how they relate to function values. Also, get the inside scoop on working with inverse functions, and don't pass on learning about applying function operations. Another concept that may have you rattled is transformations, which are also covered, including how to shift graphs on the x-y coordinate plane. We also include practice problems, so you can be sure you understand the concepts.

Let our lessons make math simple. Watch as our instructors explain all these concepts in an easy-to-follow way. Don't wait! Start watching now!

8 Lessons in Chapter 9: Properties of Functions
What is a Function: Basics and Key Terms

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.

Functions: Identification, Notation & Practice Problems

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!

Transformations: How to Shift Graphs on a Plane

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!

How to Add, Subtract, Multiply and Divide Functions

4. 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!

What Is Domain and Range in a Function?

5. 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.

How to Compose Functions

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.

Inverse Functions

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.

Applying Function Operations Practice Problems

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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