Thread: Vertical and horizontal Asymptotes.

How would you find the asymptotes of:




So far all my attempts have come up with something dealing with n/0

(I know how to do it graphically.)

Originally Posted by integral

How would you find the asymptotes of:




So far all my attempts have come up with something dealing with n/0

(I know how to do it graphically.)

when the rational function becomes undefined in this case when becomes then you have a vertical asymptote. so there is vertical asymptotes at

also, since f(x)=0 has no solutions, the graph a horizonal asymptote at y=0
if the degree of the denominator is greater that the degree of the numerator, the x-axis is the horzontal asymptote

also, what appears sometimes to be asymptotes on a graphing calculator is really just a line going from point to point where there really is a hole in the graph

Ah, I see.

So if an equation can not be set to zero then the point were it is undefined, and y=0 (if the denominator is larger than the numerator) are the asymptotes?


And just so I do not spam with more then one thread.
Could you please explain How to find points of inflections without using a graph?
Such as:

were the point of inflection would be 0

basically you find inflection points by taking the and setting x = 0

in this case

and is undefined at x=0