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

Oct 6, 2015

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

#### Explanation:

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

${\lim}_{x \to {3}^{-}} F \left(x\right) = - \infty$ and ${\lim}_{x \to 3 +} F \left(x\right) = + \infty$

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

${\lim}_{x \to \pm \infty} F \left(x\right) = 0$

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