How do you find all the asymptotes for function #2/(x-3)#?

1 Answer
Oct 6, 2015

Answer:

We have two cases to investigate: what if the denominator becomes very small, and what if #x# becomes very great?

Explanation:

If #x-3=0->x=3# the whole function becomes very great (either positive or negative, or in the "language":

#lim_(x->3^-) F(x)=-oo# and #lim_(x->3+) F(x)=+oo#

If #x# goes very great (pos or neg) the function gets smaller, or:

#lim_(x->+-oo) F(x)=0#

So the asymptotes are #x=3and F(x)=0#
graph{2/(x-3) [-10, 10, -5.005, 4.995]}