Ch 12: Rational Functions: NBPTS Math - Adolescence & Young Adult

About This Chapter

Our expert instructors developed the lessons in this chapter to get you ready for taking the National Board for Professional Teaching Standards (NBPTS) Math test for teachers of adolescence and young adult ages. This chapter covers rational functions.

Rational Functions: NBPTS Math - Adolescence & Young Adult - Chapter Summary

This chapter's lessons are short videos that provide brush up on rational functions for your NBPTS Math test. You will be prepared to answer test questions on such lesson topics as:

  • Adding and subtracting rational expressions
  • Multiplying and dividing rational expressions
  • Simplifying complex rational expressions
  • Developing expressions of rational functions
  • Solving equations and inequalities that use rational functions
  • Graphing rational functions, including those that have linear polynomials or polynomials of various degrees
  • Calculating slant asymptotes for rational functions

Lessons are usually 10 minutes or less and come with a self-assessment quiz to gauge your comprehension of the material. If you need to go back over anything in the lesson, you can use our video transcript or the timeline tool to jump right to any specific section of the video for quick replay.

9 Lessons in Chapter 12: Rational Functions: NBPTS Math - Adolescence & Young Adult
Test your knowledge with a 30-question chapter practice test
How to Add and Subtract Rational Expressions

1. 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.

How to Multiply and Divide Rational Expressions

2. 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.

Simplifying Complex Rational Expressions

3. Simplifying Complex Rational Expressions

When it comes to fractions, things may seem to get really complicated and scary when you have a fraction on top of a fraction. But never fear, after watching this video lesson, you will be able to simplify these expressions like a pro.

Expressions of Rational Functions

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.

Solving Equations & Inequalities Involving Rational Functions

5. 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.

Graphing & Analyzing Rational Functions

6. 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.

Graphing Rational Functions That Have Linear Polynomials: Steps & Examples

7. 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.

Graphing Rational Functions That Have Polynomials of Various Degrees: Steps & Examples

8. 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.

Finding Slant Asymptotes of Rational Functions

9. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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