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# Geometry/Asymptotes

Question
Hi, I have a quick question about finding horizontal and vertical asymptotes when graphing functions.

For some, like F(x) = 1/x the asymptotes are clear on the graph, but is there an equation you can use?

The assymptote on for the graph F(x) = 1/x is at x = 0.

For graphs with vertical assymptotes, they occur where x is undefined.  That is the same as where the denominator of a faction is 0, for 1/0 is undefined.  If the numerator of the fraction were also zero at this point, it might just be an undefined point on the curve.

For graphs with horizontal assymptotes, they occur where y is almost but never achieved.
To find them, evaluate the function as x goes to infinity or x goes to minus infinity.

For the graph y = x²/(x+1), there would be a vertical assymptote at x=-1, but there would also be a slanted assymptote would be at y = x.  They can be found by looking at the highest power of x in the numerator and the denominator.  In this case, it would be x²/x, which reduces to x.

Geometry

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