# Ch 17: Rational Functions and Difference Quotients: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other precalculus work.
- Identify the rational functions and difference quotients concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our high school precalculus tutoring solution will benefit any student who is trying to learn rational functions and difference quotients and earn better grades. This resource can help students including those who:

- Struggle with understanding equations and inequalities that involve rational functions, rational function graphs, the geometric interpretation of difference quotient or any other rational functions and difference quotients topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their rational functions and difference quotients unit
- Cope with ADD or ADHD
- Want to get ahead in precalculus
- Don't have access to their math teacher outside of class

## Why it works:

**Engaging Tutors:**We make learning rational functions and difference quotients simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live precalculus tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn rational functions and difference quotients on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Learn how to solve equations and inequalities involving rational functions.
- Describe how to graph and analyze rational functions.
- Examine how to find an expression for a rational function with vertical and horizontal asymptotes.
- Discover how to identify and apply the definition and geometric interpretation of 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.

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### Other Chapters

Other chapters within the High School Precalculus: Tutoring Solution course

- Working with Linear Equations: Tutoring Solution
- Working With Inequalities: Tutoring Solution
- Absolute Value Equations: Tutoring Solution
- Working with Complex Numbers: Tutoring Solution
- Systems of Linear Equations: Tutoring Solution
- Mathematical Modeling: Tutoring Solution
- Introduction to Quadratics in Precalculus: Tutoring Solution
- Working with Quadratic Functions: Tutoring Solution
- Geometry Basics for Precalculus: Tutoring Solution
- Functions - Basics for Precalculus: Tutoring Solution
- Understanding Function Operations: Tutoring Solution
- Graph Symmetry: Tutoring Solution
- Graphing with Functions: Tutoring Solution
- Rate of Change in Precalculus: Tutoring Solution
- Polynomial Functions Basics: Tutoring Solution
- Higher-Degree Polynomial Functions: Tutoring Solution
- Rational Expressions and Function Graphs: Tutoring Solution
- Exponential Functions & Logarithmic Functions: Tutoring Solution
- Using Trigonometric Functions: Tutoring Solution
- Trigonometric Graphs: Tutoring Solution
- Solving Trigonometric Equations: Tutoring Solution
- Trigonometric Identities: Tutoring Solution
- Trigonometric Applications in Precalculus: Tutoring Solution
- Graphing Piecewise Functions: Tutoring Solution
- Vectors, Matrices and Determinants: Tutoring Solution
- Mathematical Sequences and Series: Tutoring Solution
- Sets in Algebra: Tutoring Solution
- Analytic Geometry and Conic Sections: Tutoring Solution
- Polar Coordinates and Parameterizations: Tutoring Solution
- Continuity in Precalculus: Tutoring Solution
- Limits in Precalculus: Tutoring Solution