Question 150689
y= M + A/N + A
A = any coefficient
M = degree of the numerator
N = degree of the denominator 
If M = N, the horizontal asymptote is the ratio of its coefficient 
So, what if M < N and M > N, how do you find the horizontal asymptote?
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If M < N the ratio is 0; the horizontal asymptote is y = 0
Example: y = (x+2)/(x^2+4) ; ratio = 0/1 = 0
{{{graph(400,300,-10,10,-2,2,(x+2)/(x^2+4))}}}
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If M > N the ratio is "undefined"; divide to find the slant asymptote.
Example: y = (x^2+4)/(x+2) ; ratio = 1/0 = undefined
Dividing you get y = (x-2) + 8/(x^2+4)
{{{graph(400,300,-20,10,-20,10,(x^2+4)/(x+2))}}}
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Cheers,
Stan H.