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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

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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

101

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 nn and denominator dd polynomials.

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

Example: For fxx = x−2x-2x−1x-1/x−2x-2x−4x-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 fxx = x²+3x+2/x²+x-2, the process reveals a hole at 2,32,3, x-intercept at −1,0-1,0, 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 fxx = 5x−105x-10/x2+x−6x²+x-6 is analyzed showing a hole at 2,12,1, 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 DoesNotExistDoes 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

 

Algebra 2

•

101

•

Feb 21, 2023

•

4 pages

How to Graph Rational Functions with Asymptotes for Kids

user profile picture

Chelsea

@zuncho

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... Show more

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 nn and denominator dd polynomials.

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

Example: For fxx = x−2x-2x−1x-1/x−2x-2x−4x-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.

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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 fxx = x²+3x+2/x²+x-2, the process reveals a hole at 2,32,3, x-intercept at −1,0-1,0, and vertical asymptote at x = 1.

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

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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 fxx = 5x−105x-10/x2+x−6x²+x-6 is analyzed showing a hole at 2,12,1, 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 DoesNotExistDoes Not Exist is used to indicate when certain features are not present in a rational function.

Sign up to see the contentIt's free!

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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 fxx/gxx where fxx and gxx are polynomials.

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

Example: The function y = x−3x-3/x2−9x²-9 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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The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

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Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

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Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user