number of asymptotes

[cksghdrla2]

just by looking at a rational function.
how do u find the number of asymptotes?
for example, (2x^2 - 3x)/(x-2)
this one has one vertial asymptote and no horizontal asymptote but the answer said 2.
does that mean it has an oblique asymptote, if so how can u tell there are oblique asymptotes?

[AuSmith]

Yes, you need to count the horizontal, vertical, and slant (oblique) asymptotes. Here, there is one slant asymptote because the degree of the top is one more than the degree of the bottom.

[cksghdrla2]

so if degree of top is two more than bottom, then it has two oblique asymptotes?
what about when the degree of bottom is one or two higher than the degree of top?

[AuSmith]

... no. Asymptotes are lines that the graph gets arbitrarily close to. If you are just looking for a way to get the right answer without learning any math, I hope you start thirsting more for understanding. If you are already eager to learn, never mind. When the degree of the top is one more than the bottom, you can divide the polynomials and get a term that vanishes. E.g.

[unparseable or potentially dangerous latex formula]

and as [unparseable or potentially dangerous latex formula], the [unparseable or potentially dangerous latex formula] term goes to [unparseable or potentially dangerous latex formula] and the function becomes arbitrarily close to the line [unparseable or potentially dangerous latex formula]. If the difference of the degrees of the top and bottom is greater than 1, you won't get a line when you divide. If say, the top is two more than the bottom, the graph will get close to a quadratic function, which does not count as an asymptote - asymptotes are lines.

On the other hand, if the degree of the top is no greater than the bottom, you can't even have lines oblique to the [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] axes, only constant functions. And, those are not oblique because they are parallel to the [unparseable or potentially dangerous latex formula]-axis.

[stupidityismygam]

According to asymptotes are not necessarily lines?

[AuSmith]

Yea, I think we've discussed this before... apparently they are lines in UIL. If you are asking for the number of asymptotes, you can't let them be any kind of curve, because there are always uncountably many curves that are asymptotic, if any.