# Ch 10: Function Operations

### About This Chapter

## Function Operations - Chapter Summary and Learning Objectives

The video lessons in this chapter cover working with various types of functions. You'll learn about basic operations with functions and gain an understanding of one-to-one, inverse and composite functions. Other lessons show you how to graph the functions. You can assess what you've learned by working on the included practice problems. This chapter is designed to teach you to:

- Add, subtract, multiply and divide functions
- Compose functions
- Compound functions
- Understand and graph inverse functions
- Understand one-to-one functions

Video | Objective |
---|---|

How to Add, Subtract, Multiply and Divide Functions | Performing basic operations with functions. |

How to Compose Functions | Composing functions. |

Applying Function Operations Practice Problems | Gaining skill at function operations problems. |

Compounding Functions and Graphing Functions | Learning to compound and graph functions. |

Domain and Range of Composite Functions | Understanding how the domain and range of one function affects the domain and range of another function. |

Inverse Functions | Defining and understanding inverse functions. |

Understanding and Graphing Inverse Functions | Learning to graph inverse functions. |

One-to-One Functions: Definitions and Examples | Identifying one-to-one functions algebraically and graphically. Recognize relationship between domain and range of a one-to-one function and its inverse. |

### 1. 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!

### 2. 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.

### 3. 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!

### 4. Compounding Functions and Graphing Functions of Functions

We know that functions map numbers to other numbers, so what happens when you have a function of a function? Welcome to functions within functions, the realm of composite functions!

### 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

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.

### 7. Understanding and Graphing the Inverse Function

If you use a function to map a to b, is there a way to go back from b to a again? Learn how to find and graph inverse functions so that you can turn a into b and back into a.

### 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. How to Determine the Limits of Functions

You know the definition of a limit. You know the properties of limits. You can connect limits and continuity. Now use this knowledge to calculate the limits of complex functions in this lesson.

### 10. One-Sided Limits and Continuity

Over the river and through the woods is only fun on a continuous path. What happens when the path has a discontinuity? In this lesson, learn about the relationship between continuity and limits as we walk up and down this wildlife path.

### 11. Function Application for the Real World

In this lesson, we'll recall what a function is and then look at applying functions in real life that involve both numbers and objects. We'll then learn how to solve problems using these functions.

### 12. Using Quadratic Formulas in Real Life Situations

This lesson will show us how to use the quadratic formula in real-life situations. We'll look at a couple of different real-world examples of when this formula can be used to solve problems that can be modeled using quadratic equations.

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### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105