About This Chapter
How It Works:
- Identify the lessons in the McDougal Littell Rational Equations & Functions chapter with which you need help.
- Find the corresponding video lessons with this companion course chapter.
- Watch fun videos that cover the rational equations and 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:
- How to solve equations of inverse variation
- Horizontal and vertical asymptotes
- Steps to graph rational functions that have linear polynomials
- Ways to graph rational functions that have polynomials of various degrees
- Analysis of rational function graphs to find asymptotes, domain and range
- Long division and synthetic division of polynomials
- Multiplication and division of rational expressions
- Addition and subtraction of rational expressions
- Methods to solve a rational equation
McDougal Littell is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.
1. 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.
2. Horizontal and Vertical Asymptotes
No matter how hard you try to get to them, asymptotes remain out of reach. Learn about these invisible lines on graphs that show you places your equations just can't go.
3. 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.
4. 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.
5. 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.
6. How to Divide Polynomials with Long Division
Arithmetic long division and polynomial long division are very similar. Yes, it's a long process, but once you have the rhythm you will get every problem correct!
7. How to Use Synthetic Division to Divide Polynomials
Synthetic division is a 'short-cut' way of dividing a polynomial by a monomial. You still need to know long division, sorry, but this method is way fun when you're dividing by a monomial!
8. Dividing Polynomials with Long and Synthetic Division: Practice Problems
Let's look at some more polynomial division problems. We will use long division and synthetic division, but this time we will have a couple of more involved problems. So, get out some paper and a pencil and let's begin!
9. 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.
10. 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.
11. 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.
12. 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!
13. 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!
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Other chapters within the McDougal Littell Algebra 1: Online Textbook Help course
- McDougal Littell Algebra 1 Chapter 1: Expressions, Equations & Functions
- McDougal Littell Algebra 1 Chapter 2: Properties of Real Numbers
- McDougal Littell Algebra 1 Chapter 3: Solving Linear Equations
- McDougal Littell Algebra 1 Chapter 4: Graphing Linear Equations & Functions
- McDougal Littell Algebra 1 Chapter 5: Writing Linear Equations
- McDougal Littell Algebra 1 Chapter 6: Solving & Graphing Linear Inequalities
- McDougal Littell Algebra 1 Chapter 7: Systems of Linear Equations & Inequalities
- McDougal Littell Algebra 1 Chapter 8: Exponents & Exponential Functions
- McDougal Littell Algebra 1 Chapter 9: Polynomials & Factoring
- McDougal Littell Algebra 1 Chapter 10: Quadratic Equations & Functions
- McDougal Littell Algebra 1 Chapter 11: Radicals & Geometry Connections
- McDougal Littell Algebra 1 Chapter 13: Probability & Data Analysis