How do you find a vertical asymptote for a rational function?

1 Answer
Reginaldo D.
Oct 25, 2014

Let #f(x)=(p(x))/(q(x))# be a rational function. A line #x=x_0# is a vertical asymptote of #f# when

#lim_(x->x_0^+-)(p(x))/(q(x))=+-infty.#

Since a rational function is continuous in its domain, the possible vertical asymptote #x=x_0# are among that for which #q(x_0)=0#.

In other words, first we have to find a point #x_0# that is not in the domain of #f#, ie, #q(x_0)=0#, and then verify if limits of #f# are #+-infty# when x goes to #x_0^+# and #x_0^-#.

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