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

1 Answer
Sep 11, 2016

Answer:

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#