SOLUTION: I do not understand why does the graph of a rational have only one horizontal asymptote? Im familair kind of with something called an arbitrary function but that means some sort of

Question 693925: I do not understand why does the graph of a rational have only one horizontal asymptote? Im familair kind of with something called an arbitrary function but that means some sort of way it can have two functions. Im extremely confused please help me. Thank you in advance.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I do not understand why does the graph of a rational have only one horizontal asymptote? Im familair kind of with something called an arbitrary function but that means some sort of way it can have two functions. Im extremely confused please help me. Thank you in advance.
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The numerator can only have one highest power term and that term can
only have one coefficient.
----
The same is true for the denominator.
----
If the ratio of those coefficients is p/q, the horizontal asymptote
is y = p/q so long as the degree of the numerator is not greater
than the degree of the denominator.
-----
Example:
y = 3x^2/x
p/q = 3/0
No horizontal asymptote
Will have slant asymptote
---
y = x/(3x^2)
p/q = 1/3
HA: y = 1/3
-----
y = 3x^2/x^2
p/q = 3/1
HA: y = 3
==================
Cheers,
Stan H.
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