How do you find the horizontal and vertical asymptotes of a function, such as #(x+3)/(x^2-9)#?
The vertical are
and the horizontal is
The vertical asymptotes of a rational function are in the correspondence of the poles (points where the denominator is 0), because you know there the function goes to infinity on both sides (left limit and right limit) so in this case, the poles are
(I intend them as vertical lines:
The horizontal asymptotes are correlated with the limit concept: if
Totally symmetric is the case for
So you know that for