About This Chapter
Rational Expressions and Function Graphs - Chapter Summary and Learning Objectives
Fractions with polynomials in them might look intimidating, but our instructors can help you transform your understanding of linear equations and quadratics into an ability to add, subtract, multiply, and divide these rational expressions. You can also learn how to graph rational functions - regardless of whether they contain first-degree or higher-order polynomials - by determining their horizontal and vertical asymptotes and plotting points on the coordinate plane. By this chapter's end, you should be able to:
- Perform arithmetic operations with rational expressions
- Simplify and solve rational equations
- Graph rational functions containing polynomials
- Analyze a rational function's graph
|How to Multiply and Divide Rational Expressions||Learn how to factor and simplify rational expressions so you can multiply and divide them.|
|Multiplying and Dividing Rational Expressions: Practice Problems||Practice performing the steps required to multiply and divide rational expressions.|
|How to Add and Subtract Rational Expressions||Understand how to factor, find the common denominator, and simplify rational expressions in order to add and subtract them.|
|Practice Adding and Subtracting Rational Expressions||Solve practice problems to master the processes involved in adding and subtracting rational expressions.|
|How to Solve a Rational Equation||Examine procedures for finding the common denominator, releasing the denominator, simplifying, and solving rational equations.|
|Graphing Rational Functions That Have Linear Polynomials: Steps & Examples||Learn how to find the vertical and horizontal asymptotes of rational functions and plot points in order to determine their graphs.|
|Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples||Explore methods used to graph rational functions that include higher-degree polynomials.|
|Analyzing the Graph of a Rational Function: Asymptotes, Domain and Range||View sample graphs of rational functions to get practice finding horizontal and vertical asymptotes and calculating domain and range.|
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. 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.
3. 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.
4. 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!
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. 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.
7. 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.
8. 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.
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Other chapters within the Precalculus: High School course
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Introduction to Quadratics
- Working with Quadratic Functions
- Basics of Polynomial Functions
- Working with Higher-Degree Polynomials
- Graphing Piecewise Functions
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Rate of Change
- Rational Functions & Difference Quotients
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Trigonometric Graphs
- Trigonometric Applications
- Solving Trigonometric Identities
- Vectors, Matrices and Determinants
- Mathematical Sequences and Series
- Sets in Algebra
- Analytic Geometry and Conic Sections
- Polar Coordinates and Parameterizations