Asymptotes

(Sung to the tune of Jingle Bells)

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Asymptotes, Asymptotes at Infinity,
Forming Limit Barriers where Functions Cannot Be!

Asymptotes, Asymptotes, Hunting for the ‘Lines’
Horizontal, Vertical, Oblique or Special Kinds!

Traipsing Through Domains,
"What can x not be?"
Denominator Roots...Fill my Heart with Glee!
Zero Down Below...Non-zero Up Above
Indicate a Vertical Asymptote to Love!

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Let x get really big...
as big as it can be...
Where does it wind up? At infinity!
If functions are contained,
within this circumstance
A Horizontal Asymptote is there,
it's time to dance!

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With functions “rational,”
I'll check out the degree
both down-stairs and above,
a pattern now I see:
If top-heavy, divide:
an asymptote to seek.
Discard remainders...
Quotient yields a dominant oblique!