well, looking at the picture, coming from the right, namely lim -> 3⁺
starts off at 0 when x = 5, then as "x" moves to the left, it starts to go down and down and down, we have a dashed lilne at that section, namely is an asymptote, so there's a vertical asymptote at x = 3, which means that line keeps on going down to -∞.
now, coming from the left, namely lim -> 3⁻, starts off at 2 as "x" moves to the right it is going down and down and down towards the asymptotic line, so then coming from the left the limit is also -∞.
so one can say that [tex]\bf \lim\limits_{x\to 3}~ f(x) = -\infty[/tex], or it does not exist.
