About This Chapter
Who's it for?
Anyone who needs help learning or mastering high school precalculus material will benefit from taking this course. There is no faster or easier way to learn high school precalculus. Among those who would benefit are:
- Students who have fallen behind in understanding rational expressions or working with function graphs.
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about rational expressions and function graphs
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Rational Expressions and Function Graphs chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Rational Expressions and Function Graphs chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any rational expressions or function graphs question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- How do I add, subtract, multiply and divide rational expressions?
- What are the steps for solving rational equations?
- How do I graph rational functions with linear polynomials or those of various degrees?
- How do I analyze graphs of rational functions for asymptotes, 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.
9. Corresponding Angles: Definition, Theorem & Examples
In this lesson, you will learn how to identify corresponding angles. You will also learn how to use a theorem to find missing angles and solve everyday geometry problems.
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Other chapters within the High School Precalculus: Help and Review course
- Working with Linear Equations: Help and Review
- Working With Inequalities: Help and Review
- Absolute Value Equations: Help and Review
- Working with Complex Numbers: Help and Review
- Systems of Linear Equations: Help and Review
- Mathematical Modeling: Help and Review
- Introduction to Quadratics: Help and Review
- Working with Quadratic Functions: Help and Review
- Geometry Basics for Precalculus: Help and Review
- Functions - Basics for Precalculus: Help and Review
- Understanding Function Operations: Help and Review
- Graph Symmetry: Help and Review
- Graphing with Functions: Help and Review
- Rate of Change: Help and Review
- Polynomial Functions Basics: Help and Review
- Higher-Degree Polynomial Functions: Help and Review
- Rational Functions & Difference Quotients: Help and Review
- Exponential Functions & Logarithmic Functions: Help and Review
- Using Trigonometric Functions: Help and Review
- Trigonometric Graphs: Help and Review
- Solving Trigonometric Equations: Help and Review
- Trigonometric Identities: Help and Review
- Trigonometric Applications in Precalculus: Help and Review
- Graphing Piecewise Functions: Help and Review
- Vectors, Matrices and Determinants: Help and Review
- Mathematical Sequences and Series: Help and Review
- Sets in Algebra: Help and Review
- Analytic Geometry and Conic Sections: Help and Review
- Polar Coordinates and Parameterizations: Help and Review
- Continuity: Help and Review
- Limits: Help and Review