About This Chapter
Who's it for?
Anyone who needs help understanding high school precalculus material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding expressions of rational functions or working with geometric interpretations of difference quotients.
- Need an efficient way to learn about rational functions and difference quotients.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Rational Functions and Difference Quotients 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 Functions and Difference Quotients chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant 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 you solve an equation or inequality that involves a rational function?
- What steps do you follow to analyze and graph a rational function?
- How do you determine the expression of a rational function?
- What is the geometric interpretation of a difference quotient?
1. Solving Equations & Inequalities Involving Rational Functions
After watching this video lesson, you will be able to solve both equations and inequalities that involve rational functions. Learn the steps involved in solving them as well as what to watch out for.
2. Graphing & Analyzing Rational Functions
After watching this video lesson, you will be able to graph a rational function by analyzing its horizontal and vertical asymptotes. Learn to find how the graph behaves around the asymptotes.
3. Finding Slant Asymptotes of Rational Functions
Watch this video lesson to learn how you can find the slant asymptote to certain types of rational functions. Learn what you need to look for and how polynomial long division comes into play.
4. Expressions of Rational Functions
In this video lesson, you will learn how to write a rational function given just the horizontal and vertical asymptotes. Learn how to write the asymptotes and where to write them in your function.
5. The Geometric Interpretation of Difference Quotient
After watching this video lesson, you will understand how the difference quotient looks from a geometric standpoint. You will also see how the difference quotient is applied to a function.
6. Cosecant: Definition, Function & Formula
In this lesson, we will be learning about one of the six trigonometric functions. Cosecant is a function that has a very close relationship with the sine function. Let's see what their relationship is all about.
7. Slant Height: Definition & Formula
This lesson will teach you about the slant height of cones and pyramids. You will learn the formula to calculate the slant height. After the lesson, you will be able to test your knowledge with a quiz.
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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 Expressions and Function Graphs: 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