# How do you identify the horizontal asymptote of f(x) = (3)/(5x)?

May 26, 2015

Try making $x$ larger and larger and see where that leads you:

As $x$ gets larger (either positive or negative) $f \left(x\right)$ gets smaller. You can get as close to $0$ as you want, but never get there.
So $f \left(x\right) = 0$ is the horizontal asymptote .
Or in "the language"
${\lim}_{x \to \infty} \frac{3}{5 x} = 0$ and ${\lim}_{x \to - \infty} \frac{3}{5 x} = 0$

Btw: $x = 0$ is the vertical asymptote , as $x$ may not be $0$
${\lim}_{x \to {0}^{+}} \frac{3}{5 x} = \infty$ and ${\lim}_{x \to {0}^{-}} \frac{3}{5 x} = - \infty$
graph{3/(5x) [-10, 10, -5, 5]}