Slant Asymptotes

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[mighty portal]

Note that for a rational function it's very easy to at least say when it has a horizontal/slant asymptote.
Suppose R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials of degrees p and q with leading coefficients a(p) and a(q), respectively. Then there are several cases.
Case 1. p > q + 1.
There are no horizontal or slabt asymptotes.
Case 2. p = q + 1.
There is a slant asymptote with slope a(p)/a(q). The intercept can be found as usual.
Case 3. p = q.
There is a horizontal asymptote y = a(p)/a(q).
Case 4. p < q.
There is a horizontal asymptote y = 0.

[rain minnow]

Hmm right! I found vertical and horizontal very easy to understand, much easier than the slant asymptote, probably because it was easier to find material to the first two

Thanks mann

[mighty portal]

Well, to me a horizontal asymptote is just a particular case of a slant asymptote, so I sometimes I don't even think of it separately.