About This Chapter
Rational Expressions and Functions - Chapter Summary and Learning Objectives
A rational expression, also called a rational function, is a fraction with a polynomial as its numerator and denominator. The video lessons in this chapter will show you how to perform operations with rational expressions and give you practice problems to assess your skills. You'll learn to graph rational functions and analyze graphs of rational functions. At the end of this chapter, you should be able to:
- Add, subtract, multiply and divide rational expressions
- Solve a rational equation
- Understand and work with horizontal and vertical asymptotes
- Graph rational functions
- Analyze graphs of rational functions
|How to Multiply and Divide Rational Expressions||Learn to multiply and divide rational expressions.|
|Multiplying and Dividing Rational Expressions: Practice Problems||Develop skill in multiplying and dividing rational expressions.|
|How to Add and Subtract Rational Expressions||Learn to add and subtract rational expressions.|
|Adding and Subtracting Rational Expressions: Practice Problems||Develop skill in adding and subtracting rational expressions.|
|How to Solve a Rational Equation||Learn methods of solving a rational equation.|
|Horizontal and Vertical Asymptotes||Gain an understanding of horizontal and vertical asymptotes.|
|Graphing Rational Functions That Have Linear Polynomials||Graph rational functions that consist of two lineal polynomials.|
|Graphing Rational Functions That Have Polynomials of Varying Degrees||Graph rational functions that consist of polynomials of varying degrees.|
|Analyzing the Graph of a Rational Function: Asymptotes, Domain and Range||Identify asymptotes, domain and range algebraically and graphically.|
1. How to Multiply and Divide Rational Expressions
Polynomial retinal expressions, being a fraction that contains a polynomial, are able to be divided and multiplied similarly to normal fractions. Explore the extra steps involved through three examples of how to factor, flip, slash, and multiply and divide rational expressions when needed.
2. How to Add and Subtract Rational Expressions
Rational polynomial expressions are fractions with a numerator and denominator that are polynomials and can be simplified as needed and act similarly to fractions when identifying a common denominator. Learn how rational expressions are added and subtracted by simplifying through several steps demonstrated in examples.
3. How to Solve a Rational Equation
Solving a rational equation involves finding the common denominator and multiplying all numbers by it, then simplifying and checking the answer. Explore rational equations and apply the steps involved to solve example problems.
4. Horizontal and Vertical Asymptotes
Horizontal and vertical asymptotes on a graph reveal points close to the x and y axes that run on infinitely. Learn more about asymptotes, define horizontal and vertical asymptotes, and understand how asymptotes are comparable to an unreachable finish line.
5. Graphing Rational Functions That Have Linear Polynomials: Steps & Examples
A rational function with linear polynomials is a fraction of two polynomials whose highest degree is 1. Explore how to graph rational functions and discover the importance of identifying asymptotes and how to plot points.
6. Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples
Rotational Functions, fractions composed of polynomial functions, are easier to graph than they appear. Discover what is needed to graph rational functions, the steps in finding asymptotes, and how this process leads to isolating points through examples.
7. Analyzing the Graph of a Rational Function: Asymptotes, Domain, and Range
The ratio of one polynomial expression to another creates a Rational Function. Analyze the principles in graphing rational functions by isolating the domain and range, and inclusion of slant asymptotes.
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Other chapters within the Math 105: Precalculus Algebra course
- Mathematical Modeling
- Linear Equations & Inequalities
- Quadratic Functions
- Polynomial Functions of a Higher Degree
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Essentials of Trigonometry
- Introduction to the Derivative
- Studying for Math 105