# Ch 8: Holt McDougal Algebra 2 Chapter 8: Rational and Radical Functions

### About This Chapter

## How it works:

- Identify the lessons in the Holt McDougal Algebra 2 Rational and Radical Functions chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the rational and radical 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:

- Solving equations of direct and inverse variation
- Multiplying, dividing, subtracting and adding rational expressions
- Graphing rational functions that have polynomials
- Solving rational equations
- Simplifying expressions with rational exponents
- Solving radical equations

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

### 1. Solving Equations of Direct Variation

In the real world, we come across a lot of problems that vary directly with each other. You will learn how to solve these types of direct variation problems in this video lesson.

### 2. Solving Equations of Inverse Variation

After watching this video lesson, you will be able to identify problems where you can use the formula for inverse variation to solve them. Learn what is involved and how easy they are to solve.

### 3. Direct and Inverse Variation Problems: Definition & Examples

In this lesson, you'll learn how to approach questions about direct and inverse variation with a simple explanation of what the terms mean and how to apply them to problems.

### 4. How to Multiply and Divide Rational Expressions

Multiplying and dividing rational polynomial expressions is exactly like multiplying and dividing fractions. Like fractions, we will reduce. With polynomial expressions we use factoring and canceling. I also give you a little mnemonic to help you remember when you need a common denominator and when you don't.

### 5. Multiplying and Dividing Rational Expressions: Practice Problems

Let's continue looking at multiplying and dividing rational polynomials. In this lesson, we will look at a couple longer problems, while giving you some practice multiplying and dividing.

### 6. How to Add and Subtract Rational Expressions

Adding and subtracting rational expressions brings everything you learned about fractions into the world of algebra. We will mix common denominators with factoring and FOILing.

### 7. Practice Adding and Subtracting Rational Expressions

Adding and subtracting rational expressions can feel daunting, especially when trying to find a common denominator. Let me show you the process I like to use. I think it will make adding and subtracting rational expressions more enjoyable!

### 8. Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples

Graphing rational functions is not as hard or as scary as it sounds. Sure, the functions may be big, but watch this video lesson and you will see that graphing these functions can actually be easy.

### 9. Graphing Rational Functions That Have Linear Polynomials: Steps & Examples

Watch this video lesson to learn how you can graph rational functions with linear polynomials in just a few steps. Also learn what kinds of functions these are and what you need to look for to graph them.

### 10. Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range

A rational function arises from the ratio of two polynomial expressions. The graphs of rational functions often have distinct characteristics. In this lesson, we look at how to analyze some of those characteristics.

### 11. Transformations of the 1/x Function

In this lesson, you'll learn about the function f(x) = 1/x. You'll also learn about the different transformations that can be applied to the equation to change the graph of this function.

### 12. How to Solve a Rational Equation

A rational equation is one that contains fractions. Yes, we will be finding a common denominator that has 'x's. But no worries! Together we will use a process that will help us solve rational equations every time!

### 13. Rational Equations: Practice Problems

Mario and Bill own a local carwash and have several complex tasks that they must use rational equations to solve for an answer. Enjoy learning how they solve these equations to help them with some of their day-to-day tasks.

### 14. Solving Rational Inequalities

Rational inequalities show up often in areas such as engineering, medicine, and finance. This lesson will use a real life example to demonstrate a step-by-step process used to solve these types of inequalities.

### 15. Rational Exponents

In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.

### 16. Simplifying Expressions with Rational Exponents

Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!

### 17. What is a Radical Function? - Definition, Equations & Graphs

Radical functions operate very differently than regular functions. This lesson covers the definitions, equations, and graphs that you will need to know to be successful with radical functions.

### 18. Transformations of Radical Functions

A radical function is a function with a square root or other radical in it. Learn how changes to the equations of radical functions map onto changes in the graphs of the functions in this lesson.

### 19. Solving Radical Equations: Steps and Examples

Solving radical equations is not any more difficult than solving other algebraic equations. This lesson will show you how to solve equations containing a square root and give some real-world examples.

### 20. Solving Radical Equations with Two Radical Terms

Solving equations with two radical terms takes some patience and care, but it really is not difficult. This lesson will show you the steps to solve these more complicated equations plus give you some examples to follow.

### 21. Solving Radical Inequalities

This lesson will show how to solve radical inequalities using radical definitions and properties. Key terms and radical notes are included to share step by step the method to solve these special types of inequalities.

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### 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 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