# Ch 1: Holt McDougal Algebra 2 Chapter 1: Foundations for Functions

### About This Chapter

## How it works:

- Identify the lessons in Holt McDougal Algebra 2 Foundations for Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the foundations for 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 about:

- Working with different types of numbers or subsets
- Using set builder notation to write sets
- Applying the commutative property
- Finding the square root of a number
- Factoring radical expressions
- Simplifying square roots of quotients
- Adding and subtracting with radical notation
- Translating words into algebraic expressions
- Evaluating simple algebraic expressions
- Combining like terms
- Simplifying and solving exponential expressions
- Using scientific notation
- Identifying domain and range in functions
- Shifting graphs on a plane

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

### 1. What are the Different Types of Numbers?

Learn all of the different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. This video lesson teaches you how to classify any numbers you come across.

### 2. Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty)

In this video, we will add to our knowledge of sets. We will talk about cardinality, infinite, finite, equal and the empty set. I think you will find these very straightforward, so let's begin.

### 3. How to Write Sets Using Set Builder Notation

Set builder notation allows the user to indicate specific items that are to be included within a set. In this lesson, we will learn how to write sets using set builder notation.

### 4. Interval Notation: Definition & Examples

This lesson defines interval notation and explains how to write sets in interval notation. It also explores the various types of intervals, including open and closed intervals.

### 5. Introduction to Groups and Sets in Algebra

As an introduction to the algebraic concepts of sets and groups, this lesson covers the difference between the two concepts and how to determine if a set is a group. To complete this lesson, we'll take a look at some practice examples.

### 6. The Commutative Property: Definition and Examples

There are three major properties that deal with the addition and multiplication of numbers. One of those properties is the commutative property. This lesson will define and give examples of the commutative property and how it works.

### 7. How to Find the Square Root of a Number

What is a square root? In this lesson, we'll learn what a square root is and how to find it. We'll review a variety of examples in order to master the concept.

### 8. Factoring Radical Expressions

Watch this video lesson to learn how to apply the product rule to your radical expressions. Learn how this product rule actually helps you to simplify your radicals as well.

### 9. Simplify Square Roots of Quotients

The quotient rule can be used to simplify square roots of quotients. This lesson will define the quotient rule and show you how it is used to simplify square roots.

### 10. Addition and Subtraction Using Radical Notation

There are specific rules governing adding and subtracting radical expressions. This lesson will describe these rules and give examples of how they are used.

### 11. Translating Words to Algebraic Expressions

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

### 12. Evaluating Simple Algebraic Expressions

In this lesson, we'll learn how to evaluate algebraic expressions, which involves substituting numbers for variables and following the order of operations. By the end of the lesson, you'll be an algebraic expression expert.

### 13. Combining Like Terms in Algebraic Expressions

When you have an algebraic expression that's much too long, it would be great if you could simplify it. That's when knowing how to combine like terms comes in. In this lesson, we'll learn the process of combining like terms and practice simplifying expressions.

### 14. Simplifying and Solving Exponential Expressions

What do we do with an exponent? In this lesson, we'll learn how to simplify and solve expressions containing exponents. We'll solve a variety of types of exponential expressions.

### 15. What Are the Five Main Exponent Properties?

We'll look at the five important exponent properties and an example of each. You can think of them as the order of operations for exponents. Learn how to handle math problems with exponents here!

### 16. How to Define a Zero and Negative Exponent

The zero and negative exponent properties are two you will use quite a lot in mathematics. The negative exponent property can be confusing, but when you remember a couple fun ideas, you will get it right every time!

### 17. How to Simplify Expressions with Exponents

In this video, we will put all of the exponent properties we have learned together. Don't let lots of numbers and letters confuse you! Simplifying exponents can be easy and fun!

### 18. Scientific Notation: Definition and Examples

Scientific notation is a special way of writing numbers so they are easier to work with. This lesson will define scientific notations and show some examples of how to convert numbers from standard notation to scientific notation and back.

### 19. 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!

### 20. 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.

### 21. 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.

### 22. 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!

### 23. How to Graph Reflections Across Axes, the Origin, and Line y=x

A graph can be reflected in three ways - across the axes, the origin and the line y = x. There are specific rules to perform each reflection. This lesson will describe those rules and show you how to perform these reflections.

### 24. Stretching & Compressing a Function

Learn about the changes to a function that can ether stretch or compress the graph of that function. This lesson covers horizontal and vertical changes, including both stretching and compression.

### 25. Parent Functions: Graphs & Examples

In this lesson, you're going to learn about the difference between a family of functions, the parent function, and the graphic and mathematical representations of important parent functions.

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### Other Chapters

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

- 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 9: Properties and Attributes of 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