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17. Rational Functions

17. Rational Functions

Learn about 17. Rational Functions and discover its key concepts through interactive lessons and practical exercises.

Sections

What is a Rational Function?

A rational function is defined as a ratio of two polynomial functions, with its denominator not equal to zero.

1 Section Overview

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Domain of Rational Functions

The domain of a rational function is defined by the values of the variable that do not make the denominator equal to zero.

2 Section Overview

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Simplifying Rational Expressions

This section provides a detailed methodology for simplifying rational expressions by factoring and canceling common factors.

3 Section Overview

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Vertical and Horizontal Asymptotes

This section discusses vertical and horizontal asymptotes of rational functions, explaining how they are determined based on the function's equation and its polynomial degree.

4 Section Overview

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4.1 Vertical Asymptotes

Vertical asymptotes occur at values of x that make the denominator of a rational function equal to zero after simplification.

4.2 Horizontal Asymptotes

This section introduces horizontal asymptotes in rational functions, detailing their significance based on polynomial degrees.

Holes in the Graph

Holes in the graph of rational functions occur when a factor in the denominator cancels with a factor in the numerator.

5 Section Overview

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Intercepts

This section describes how to find the x-intercept and y-intercept of rational functions.

6 Section Overview

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6.1 x-intercept

The x-intercept of a function is found by setting the function equal to zero and solving for x.

6.2 y-intercept

The y-intercept of a function is the point where the graph intersects the y-axis, found by evaluating the function at x=0.

Graphing Rational Functions

This section covers how to graph rational functions, focusing on essential components such as domain, asymptotes, and intercepts.

7 Section Overview

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Solving Rational Equations

This section focuses on solving equations that involve rational expressions, guiding through the identification of restrictions, the use of least common denominators, and verifying solutions.

8 Section Overview

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Summary

This section encapsulates the key concepts associated with rational functions, including their definitions, domains, simplifications, asymptotes, and graphing techniques.

9 Section Overview

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Learning Objectives

  • Master the fundamentals of 17. Rational Functions

  • Apply learned concepts in practical scenarios

  • Successfully complete all chapter exercises

Practice Exercises

Total Questions

4

Estimated Time

8 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting