# Ch 9: Holt McDougal Algebra 2 Chapter 9: Properties and Attributes of Functions

### About This Chapter

## How it works:

- Identify the lessons in the Holt McDougal Algebra 2 Properties and Attributes of Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the properties and attributes of functions 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:

- Graphs of basic functions
- Piecewise functions
- Addition, subtraction, multiplication and division of functions
- Domain and range of composite functions
- Inverse functions
- One-to-one functions

*Holt McDougal is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Graphing Basic Functions

Graphs are just like maps - when you know the language! Review how locations have x and y coordinates similar to latitude and longitude, and how to plot points in the Cartesian plane.

### 2. What are Piecewise Functions?

A piecewise function is a certain type of function that is made up of different parts. This lesson will define and describe piecewise functions and teach you how to identify them and how to write them.

### 3. How to Graph Piecewise Functions

Piecewise functions are specific functions that have more than one piece. There is a special trick to graphing these type of functions, which you will learn in this lesson.

### 4. Step Function: Definition, Equation & Examples

In this lesson, we'll learn what a step function is and become comfortable with this type of function. We'll examine common examples, such as the floor and ceiling functions and the heaviside function.

### 5. Translating Piecewise Functions

Piecewise functions are two or more functions that only use part of a domain. If these functions need to be changed, we can translate them without even having to know the equation.

### 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. 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!

### 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!

### 9. 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.

### 10. 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.

### 11. 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.

### Earning College Credit

Did you know… We have over 200 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

Other chapters within the Holt McDougal Algebra 2: Online Textbook Help course

- Holt McDougal Algebra 2 Chapter 1: Foundations for Functions
- Holt McDougal Algebra 2 Chapter 2: Linear Functions
- Holt McDougal Algebra 2 Chapter 3: Linear Systems
- Holt McDougal Algebra 2 Chapter 4: Matrices
- Holt McDougal Algebra 2 Chapter 5: Quadratic Functions
- Holt McDougal Algebra 2 Chapter 6: Polynomial Functions
- Holt McDougal Algebra 2 Chapter 7: Exponential and Logarithmic Functions
- Holt McDougal Algebra 2 Chapter 8: Rational and Radical Functions
- Holt McDougal Algebra 2 Chapter 10: Conic Sections
- Holt McDougal Algebra 2 Chapter 11: Probability and Statistics
- Holt McDougal Algebra 2 Chapter 12: Sequences and Series
- Holt McDougal Algebra 2 Chapter 13: Trigonometric Functions
- Holt McDougal Algebra 2 Chapter 14: Trigonometric Graphs and Identities