# Ch 18: Rational Expressions and Function Graphs: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other precalculus work.
- Identify the rational expressions and function graphs 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 expressions and function graphs and earn better grades. This resource can help students including those who:

- Struggle with understanding multiplying and dividing rational expressions, adding and subtracting rational expressions, graphing rational functions with linear polynomials or any other rational expressions and function graphs 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 Expressions and Function Graphs 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 expressions and function graphs 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 expressions and function graphs 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

- Multiply and divide rational expressions.
- Add and subtract rational expressions.
- Solve rational equations.
- Graph rational functions that have linear polynomials.
- Graph rational functions that have polynomials of various degrees.
- Analyze the 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

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 Functions and Difference Quotients: 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