# How do you find the vertical, horizontal or slant asymptotes for f(x) = -(1/x)?

Sep 11, 2016

The VA is $x = 0$ and the HA is $y = 0$.

#### Explanation:

$f \left(x\right) = - \frac{1}{x}$

Vertical asymptote(s) are found by setting the denominator equal to zero.

VA: $x = 0$

Horizontal and slant asymptotes are found using the 3 HA rules.

If degree of denominator > degree of numerator, the HA is $y = 0$.

If degree of denominator = degree of numerator, the HA is the
leading coefficient of the numerator divided by the leading coefficient of the denominator.

If degree of the denominator < degree of numerator, there is a slant asymptote.

In this example, the degree of the numerator is zero and the degree of the denominator is one, so we use the first rule, and the HA is $y = 0$