Question

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

Answer 1

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

Explanation:

`f(x)=-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`