# Ch 4: Understanding Relations & Functions

### About This Chapter

## Understanding Relations and Functions - Chapter Summary

The material in this chapter can be utilized to enhance your understanding of relations and functions. You'll have fun viewing our entertaining video lessons as you refresh your knowledge of this topic. You can study such competencies as function notation, domain and range of composite functions, and inverse functions. Once you have covered the material in these lessons, you should have the knowledge to:

- Define what a relation is in math
- Describe the difference between relations and functions
- Identify functions and solve problems with functions
- Compare properties of functions algebraically, graphically, and numerically
- Use operations to solve functions
- Show how to compose functions
- Graph an inverse function

These lessons have quizzes accompanying them so you can quickly ascertain your understanding of the information you just reviewed. If you need to take another look, you can easily jump to a certain spot by using the lesson timeline or using the links in the quiz. Subject-matter experts are just a query away if you need to ask for help or clarification. The convenience and flexibility of this study can help you quickly reach your goals.

### 1. Relation in Math: Definition & Examples

In this lesson, you will learn the definition of relation in terms of mathematics, as well as the various ways of displaying relations. We will also look at some examples.

### 2. The Difference Between Relations & Functions

Relations and functions are a huge part of mathematics. In this lesson, we will define relations and functions. We will look at the differences between the two and how to determine whether a given relation is a function.

### 3. 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!

### 4. Compare Properties of Functions Algebraically

In this lesson, we will explore algebraic and numeric properties and the evaluation of functions. We'll demonstrate function evaluations and the idea that every element of the domain has a unique element in the range.

### 5. Compare Properties of Functions Graphically

In this lesson, we will cover the characteristics of graphs of functions. We will employ the vertical line test and understand why some graphs do not qualify as functions.

### 6. Compare Properties of Functions Numerically

Can you compare functions when they're written out numerically as tables of values? In this lesson, you'll learn to do just that and to compare one function as a table to another written in a different form.

### 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. 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.

### 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. 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.

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### Other Chapters

Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course

- Overview of Mathematical Reasoning
- Introduction to Mathematical Problem Solving
- NES Math: Properties of Real Numbers
- Overview of Linear Functions & Equations
- Quadratic Equations, Functions & Inequalities
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Probability: Principles & Techniques
- Overview of Discrete Mathematics
- Performing Operations on Matrices & Vectors
- Solving Problems with Sequences & Series
- NES Mathematics Middle Grades & Early Secondary Flashcards