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How to Graph Rational Functions with Asymptotes for Kids

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Chelsea

2/21/2023

Algebra 2

Graphing Rational Functions

Subjects

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Algebra 2

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Transformations

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Graphs of Square and Cube Root Functions

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Radical Functions & Their Graphs

How to Graph Rational Functions with Asymptotes for Kids

Graphing Rational Functions - A comprehensive guide to understanding and plotting rational functions through asymptotes, intercepts, and branches.

  • Learn to identify and analyze steps to find horizontal and vertical asymptotes in rational functions
  • Master techniques for solving rational function intercepts and branches
  • Understand how to determine holes and plot complete rational function graphs
  • Explore the relationship between polynomial degrees and asymptotic behavior
  • Practice with multiple examples of increasing complexity in rational function graphing
...

2/21/2023

99

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

View

Page 2: Understanding Horizontal Asymptotes

This page details the process of finding horizontal asymptotes through degree comparison between numerator and denominator polynomials.

Definition: Horizontal asymptotes are determined by comparing the degrees of numerator (n) and denominator (d) polynomials.

Highlight: There can only be one horizontal asymptote maximum for any rational function.

Example: For f(x) = (x-2)(x-1)/(x-2)(x-4), after cancellation, the horizontal asymptote is y = 1.

Quote: "If you big on top, just stop!" - referring to when the numerator degree exceeds the denominator degree.

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

View

Page 3: Systematic Approach to Graphing Rational Functions

This page outlines a comprehensive seven-step process for graphing rational functions effectively.

Highlight: The systematic approach includes factoring, finding holes, intercepts, asymptotes, and sketching branches.

Example: For f(x) = x²+3x+2/x²+x-2, the process reveals a hole at (2,3), x-intercept at (-1,0), and vertical asymptote at x = 1.

Definition: A hole occurs in a rational function when the same factor cancels in both numerator and denominator.

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

View

Page 4: Advanced Examples and Applications

This page provides multiple complex examples demonstrating the complete process of analyzing and graphing rational functions.

Example: The function f(x) = (5x-10)/(x²+x-6) is analyzed showing a hole at (2,1), vertical asymptote at x = -3, and horizontal asymptote at y = 0.

Highlight: Each example demonstrates different combinations of features including holes, asymptotes, and intercepts.

Vocabulary: DNE (Does Not Exist) is used to indicate when certain features are not present in a rational function.

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Subjects

/

Algebra 2

/

Transformations

/

Graphs of Square and Cube Root Functions

/

Radical Functions & Their Graphs

How to Graph Rational Functions with Asymptotes for Kids

user profile picture

Chelsea

@zuncho

·

635 Followers

Follow

Graphing Rational Functions - A comprehensive guide to understanding and plotting rational functions through asymptotes, intercepts, and branches.

  • Learn to identify and analyze steps to find horizontal and vertical asymptotes in rational functions
  • Master techniques for solving rational function intercepts and branches
  • Understand how to determine holes and plot complete rational function graphs
  • Explore the relationship between polynomial degrees and asymptotic behavior
  • Practice with multiple examples of increasing complexity in rational function graphing
...

2/21/2023

99

 

Algebra 2

4

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

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Page 2: Understanding Horizontal Asymptotes

This page details the process of finding horizontal asymptotes through degree comparison between numerator and denominator polynomials.

Definition: Horizontal asymptotes are determined by comparing the degrees of numerator (n) and denominator (d) polynomials.

Highlight: There can only be one horizontal asymptote maximum for any rational function.

Example: For f(x) = (x-2)(x-1)/(x-2)(x-4), after cancellation, the horizontal asymptote is y = 1.

Quote: "If you big on top, just stop!" - referring to when the numerator degree exceeds the denominator degree.

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 3: Systematic Approach to Graphing Rational Functions

This page outlines a comprehensive seven-step process for graphing rational functions effectively.

Highlight: The systematic approach includes factoring, finding holes, intercepts, asymptotes, and sketching branches.

Example: For f(x) = x²+3x+2/x²+x-2, the process reveals a hole at (2,3), x-intercept at (-1,0), and vertical asymptote at x = 1.

Definition: A hole occurs in a rational function when the same factor cancels in both numerator and denominator.

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 4: Advanced Examples and Applications

This page provides multiple complex examples demonstrating the complete process of analyzing and graphing rational functions.

Example: The function f(x) = (5x-10)/(x²+x-6) is analyzed showing a hole at (2,1), vertical asymptote at x = -3, and horizontal asymptote at y = 0.

Highlight: Each example demonstrates different combinations of features including holes, asymptotes, and intercepts.

Vocabulary: DNE (Does Not Exist) is used to indicate when certain features are not present in a rational function.

480/81 Day 1 Notes OBJECTIVES: 1) Determine vertical and horizontal asymptotes and x and y intercepts to graph rational functions. RATIONAL

Sign up to see the content. It's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Page 1: Introduction to Rational Functions and Asymptotes

This page introduces the fundamental concepts of rational functions and their key components. A rational function is explained as a ratio of two polynomials, with emphasis on branches and asymptotes.

Definition: A rational function is expressed as f(x)/g(x) where f(x) and g(x) are polynomials.

Highlight: A rational function has one more branch than the number of vertical asymptotes.

Example: The function y = (x-3)/(x²-9) demonstrates vertical asymptotes at x = -3 and x = 3.

Vocabulary: Branches refer to the continuous portions of a rational function graph separated by vertical asymptotes.

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Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

20 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying