MHB What are the steps for finding asymptotes of rational functions?

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To find asymptotes of rational functions, one must identify vertical, horizontal, and oblique asymptotes. Vertical asymptotes occur at values that make the denominator zero, while horizontal asymptotes are determined by the degrees of the numerator and denominator. Oblique asymptotes appear when the degree of the numerator is one greater than that of the denominator. The discussion emphasizes the classification of asymptotes, including higher-order types like quadratic and cubic. Overall, understanding these concepts is crucial for analyzing rational functions effectively.
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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.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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