# 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?

Numbers are classified into different types. Learn how to identify and classify natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

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

Sets are a collection of objects that have a similar quality, and the number of elements of a set is referred to as the cardinality of the set. Learn about sets, the difference between infinite and finite sets, the difference between equal and equivalent sets, and how to determine the cardinality of a set.

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

In math, set notation defines the criteria and properties of a set using symbols. Learn what set notation is, explore set notation with numbers, and discover how to write sets using set builder notation.

### 4. Interval Notation: Definition & Examples

Interval notation is the use of rectangular brackets or parenthesis enclosing two endpoints of an interval. Learn about the definition and examples of an interval notation, and understand how to write sets in interval notation.

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

Sets and groups are descriptive terms used in algebra for a collection of any items or elements. Learn about the definition of sets and groups, numerical sets, group operations, group rules through a series of examples.

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

The commutative property in mathematics asserts that terms in an equation can be swapped, and still have the same answer. Learn the implications of this principle, and how to use it in examples problems.

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

Calculating the square root of a number is the inverse operation of squaring that number. Explore how to find square roots, the square of numbers, perfect and imperfect squares, and some square root practice examples.

### 8. Factoring Radical Expressions

Radical expressions can be factored by following the product rule for radicals. Learn about radical expressions, how to identify and factor them, and how to apply the product rule to simplify a radical expression.

### 9. Simplify Square Roots of Quotients

The quotient rule can be used to solve radical expressions. This lesson explores this idea and provides examples demonstrating how to simplify the square roots of quotients.

### 10. Addition and Subtraction Using Radical Notation

In mathematics, a radical notation indicates the square root of a number. Learn how to do addition and subtraction using radical notation, and recognize that mathematics and algebra include terms that may not be like others though radicals are regarded as like terms.

### 11. Translating Words to Algebraic Expressions

In mathematics, word problems can be easier to calculate when they are written as algebraic expressions. Learn how to translate word problems, and explore words and terms related to addition, subtraction, multiplication, division, and equal operations to be able to accurately translate math word problems.

### 12. Evaluating Simple Algebraic Expressions

To evaluate simple algebraic expressions, substitute a number for each variable and solve. Learn the steps for evaluating simple algebraic expressions, including rules for order of operations and parentheses, and tackle the practice problems in this lesson.

### 13. Combining Like Terms in Algebraic Expressions

Combining like terms, which refers to the process of merging terms that have the same variable, is a way to simplify algebraic expressions. Learn what combining like terms means, understand the process of adding variables, and review practice problems.

### 14. Simplifying and Solving Exponential Expressions

Exponential expressions display how many times a number can be multiplied by itself. Learn how to simplify exponential expression problems, examine the functions of an exponent, how it affects positive and negative integers, and solve some sample exponential expressions.

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

Exponents have several properties which are used to rewrite expressions and simplify them. Learn about exponents and the five main properties used for simplifying exponential expressions.

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

Exponents of mathematical terms and expressions can be negative numbers or zero. Learn about zero and negative exponents, and how to use their properties in simplifying expressions.

### 17. How to Simplify Expressions with Exponents

Expressions with exponents can be simplified using the following properties: Product of Powers, Power to a Power, Quotient of Powers, Power of a Product, and the Zero Property. Learn to simplify expressions with exponents by solving practice problems included in this lesson.

### 18. Scientific Notation: Definition and Examples

Scientific Notation is the method of expressing very large or small numbers with exponents instead of a series of '0's. Discover how scientific notation is used, and examples to discern the difference in writing positive vs negative exponents.

### 19. Functions: Identification, Notation & Practice Problems

A function is an equation that plugs in one thing to get another thing. Discover the difference between a regular equation and a function, function notation, and how to spot a function graphically using the vertical line test and practice problems.

### 20. What Is Domain and Range in a Function?

When describing functions, the set of potential inputs is the domain, and the set of potential outputs is the range. Learn how to determine the domain and range from a graph, as well as by exploring the rule of the function alone.

### 21. What is a Function: Basics and Key Terms

Functions are mathematical methods of determining a set of numbers that is dependent on another set of numbers. This lesson explores the basics and key terms of a function and demonstrates how functions can be mapped onto graphs.

### 22. Transformations: How to Shift Graphs on a Plane

Mathematical transformations are functions that change into different functions. Explore the four types of transformations to include: rotations, reflections, dilations, and translations, and take a closer look at how to shift graphs on a plane.

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

Reflections on a graph appear as they sound literally, where a given graph is 'flipped' along to to appear in the equal opposite distance from the given line as the original. Learn the rules in how graphs are reflected across axes, the origin, and line y=x.

### 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