About This Chapter
Who's it for?
This unit of our High School Trigonometry Homeschool Curriculum course will benefit any student who is trying to learn about function graphs. There is no faster or easier way to learn how to graph a rational function. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn about rational expressions, equations and functions.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a math curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a Function Graphs unit exam confirm understanding or identify any topics that require review.
Function Graphs Unit Objectives:
- Add, subtract, multiply and divide rational expressions.
- Understand the process for solving rational equations.
- Graph rational functions with linear polynomials.
- Graph rational functions with polynomials of different degrees.
- Read and evaluate graphs of rational functions.
- Identify domain, range and asymptotes on graphs of rational functions.
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 High School Trigonometry: Homeschool Curriculum course
- Types of Real Numbers: Homeschool Curriculum
- Working with Linear Equations: Homeschool Curriculum
- Graphing Inequalities: Homeschool Curriculum
- Absolute Value Equations: Homeschool Curriculum
- Complex Numbers: Homeschool Curriculum
- Using Systems of Linear Equations: Homeschool Curriculum
- Mathematical Modeling: Homeschool Curriculum
- Introduction to Quadratics: Homeschool Curriculum
- Quadratic Functions: Homeschool Curriculum
- Coordinate Geometry: Homeschool Curriculum
- Functions for Trigonometry: Homeschool Curriculum
- Function Operations: Homeschool Curriculum
- Graph Symmetry: Homeschool Curriculum
- Graphing with Functions: Homeschool Curriculum
- Polynomial Functions Basics: Homeschool Curriculum
- Higher-Degree Polynomial Functions: Homeschool Curriculum
- Difference Quotients: Homeschool Curriculum
- Exponential Functions: Homeschool Curriculum
- Trigonometric Functions: Homeschool Curriculum
- Triangle Trigonometry: Homeschool Curriculum
- Trigonometric Graphs: Homeschool Curriculum
- Solving Trigonometric Equations: Homeschool Curriculum
- Trigonometric Identities: Homeschool Curriculum
- Trigonometric Applications: Homeschool Curriculum
- Analytic Geometry: Homeschool Curriculum
- Vectors, Matrices & Determinants: Homeschool Curriculum
- Polar Coordinates: Homeschool Curriculum
- Circular Arcs, Circles & Angles: Homeschool Curriculum