How would you find the asymptotes of:
$\displaystyle y=\frac{1}{x^2-1}$
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 $\displaystyle x^2-1 $becomes $\displaystyle 0$ then you have a vertical asymptote. so there is vertical asymptotes at $\displaystyle \pm1$
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:
$\displaystyle \sqrt[3]{x}$ were the point of inflection would be 0