About This Chapter
Rational Functions & Expressions - Chapter Summary
Watch entertaining lessons developed by subject-matter experts to explore ways to solve, simplify, analyze and graph rational functions and expressions. This chapter provides steps for performing these mathematical operations and also offers examples to illustrate these steps. Once you've completed this chapter, you will be ready for the following:
- Multiplying, dividing, adding and subtracting rational expressions
- Dividing and taking the reciprocal of any rational expression
- Demonstrating how to simplify complex rational expressions
- Solving a rational equation
- Exhibiting an ability to analyze a graph of a rational function
- Showing how to solve equations of direct and inverse variation
- Graphing rational functions with linear polynomials and polynomials of various degrees
The videos in this chapter average about 10 minutes apiece, providing you with access to short, detailed lessons you can easily incorporate into your daily routine. Watch the lessons in any sequence and as often as needed to feel confident that you comprehend rational functions and expressions. Full transcripts of the lessons are available that feature easy-to-identify vocabulary words. If you want to test your knowledge of the lessons, be sure to take the self-assessment quizzes and practice exam for this chapter.
1. 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.
2. 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.
3. Division and Reciprocals of Rational Expressions
In this video lesson, you will learn how to divide and take the reciprocal of any rational expression. Learn the one easy step you take to be able to find your answer quickly and easily.
4. Simplifying Complex Rational Expressions
When it comes to fractions, things may seem to get really complicated and scary when you have a fraction on top of a fraction. But never fear, after watching this video lesson, you will be able to simplify these expressions like a pro.
5. 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!
6. 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.
7. 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.
8. 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.
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. 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.
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Other chapters within the STAAR Algebra II: Test Prep & Practice course
- Complex and Imaginary Numbers
- Calculating & Simplifying Exponential Expressions
- Understanding Polynomial Functions
- Solving Algebraic Equations Overview
- Operations with Radical Expressions
- The Basics of Functions
- Graphing Functions Overview
- Solving & Graphing Systems of Equations
- Solving & Graphing 1 & 2 Variable Inequalities
- Solving & Graphing Quadratics
- Quadratics & Higher Order Polynomials
- Solving Exponential & Logarithmic Functions
- Absolute Value Equations
- About the STARR Tests
- STAAR Algebra II Flashcards