About This Chapter
Rational Functions & Difference Quotients - Chapter Summary and Learning Objectives
Understanding rational functions and difference quotients doesn't have to be an overwhelming process. This chapter offers fun video lessons with short quizzes for self-assessment to make this a pleasant learning experience. First, you can find out how to solve equations and inequalities with rational functions, and then you'll learn the steps for graphing rational functions. Need to learn more about difference quotients? You can also practice finding and using their geometric interpretation through these short, user-friendly lessons. In this chapter, you'll get experience with the following concepts:
- Solving inequalities and equations that involve rational functions
- Graphing rational functions
- Finding expressions for rational functions
- Using the geometric interpretation of difference quotients
|Solving Equations & Inequalities Involving Rational Functions||This lesson discusses how to solve equations and inequalities that include rational functions.|
|Graphing & Analyzing Rational Functions||This lesson explains how to graph rational functions in factored form with zeros. Point out the asymptotes and test the intervals.|
|Expressions of Rational Functions||Discover rational functions by using the horizontal and vertical asymptotes.|
|The Geometric Interpretation of Difference Quotient||Explore the geometric interpretation of difference quotient. Simplify and explain the quotients using rates of change and slopes of secant lines.|
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.
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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 Expressions and Function Graphs
- 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