Monday, November 20, 2006

4.5 Slant Asymptotes

I was having trouble editing my other post, so i created a new one for the stuff we learned today dealing with slant asymptotes. If you're like me, you never learned about long division involving a variable. Its very similar to normal long division.
First, I'll tell you about the application of long division. In rational functions, slant asymptotes occur when the degree(highest exponent) of the numerator is one larger than the degree of the denominator. A slant asymptote is a linear function (following the form y =mx + b) that is never reached by the function.

So a function can have no vertical or horizontal asymptotes, but it might have a slant asymptote.
To find the slant asymptote, use long division. For example: ( 2 - 3x^2)/(x-1)

start by setting the equation up as a normal long division problem.
to learn how to do long division go to this very helpful site (they explain it better than i can):

the result is -3x-3 + (-1/(x-1))
you only use the -3x-3 part of this because the rest is a remainder.
Therefore, the slant asymptote is y = -3x - 3


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