About This Chapter
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!
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. 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!
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.
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!
Earning College Credit
Did you know… We have over 160 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 Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Complex and Imaginary Numbers
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Logarithms and Exponential Equations
- Probability and Statistics
- Studying for Math 102