Question

3/x-2, i'm confused as to what the horizontal asymptote is. The resources I found online conclude that it has a horizontal asymptote of y=0. I know that in order for a horizontal asymptote to be y=0, the denominator has to have a greater degree than the numerator. Im confused because doesn't the numerator have the same degree as the denominator (degree of 1)?

Answer 1

The Horizontal Asymptote is at x=3

Explanation:

Here is a way to remember this

One way to remember this is the following pnemonic device: BOBO BOTN EATS DC

EABOBO -Exponents are bigger on bottom, y=0

EABOTN -Exponents are bigger on top, none

EATS DC - Exponents are the same, divide coefficients

3/x-2 the exponents are the same, divide leading coefficients

3/1 = 3 the horizontal asymtote is at x=3