What are the steps for finding asymptotes of rational functions?

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SUMMARY

The discussion focuses on identifying asymptotes of rational functions, specifically highlighting three main types: vertical, horizontal, and oblique asymptotes. Vertical and horizontal asymptotes are the most commonly recognized, while oblique asymptotes are defined as linear asymptotes that do not fall into the vertical or horizontal categories. Additionally, asymptotes can be classified into higher-order types, such as quadratic, cubic, quartic, and quintic. The conversation emphasizes the importance of understanding these classifications for a comprehensive grasp of rational functions.

PREREQUISITES
  • Understanding of rational functions
  • Familiarity with polynomial equations
  • Knowledge of limits in calculus
  • Basic algebra skills
NEXT STEPS
  • Study the process of finding vertical asymptotes in rational functions
  • Learn how to determine horizontal asymptotes using limits
  • Explore the concept of oblique asymptotes and their derivation
  • Investigate higher-order asymptotes and their classifications
USEFUL FOR

Students studying calculus, mathematics educators, and anyone seeking to deepen their understanding of rational functions and their asymptotic behavior.

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Hello everyone. Time to get back to math. I have forgotten how to find asymptotes of rational functions. I think there are three types of asymptotes. Can someone show me how to find asymptotes of rational functions? What exactly is an asymptote?
 
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RTCNTC said:
Hello everyone. Time to get back to math. I have forgotten how to find asymptotes of rational functions. I think there are three types of asymptotes. Can someone show me how to find asymptotes of rational functions? What exactly is an asymptote?

There are many types of asymptotes. It depends on how you wish to classify them.

Vertical and Horizontal are the most easily recognized.

Oblique is next. Just a linear asymptote that is neither Vertical nor Horizontal.

After that, it is possible to group into just "Higher Order", or you may wish to classify as Quadratic, Cubic, Quartic, Quintic, etc.

We stretch the definition of Rational Function a little if we find anything other than a polynomial asymptote.
 
I will post 3 questions tonight involving all three asymptotes.
 

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