Question

How do you find the horizontal asymptote for `(x-3)/(x-2)`?

Answer 1

Let `f(x) = (x-3)/(x-2)`.

Since the degree of the numerator and the denominator are both the same, namely `1`, then the horizontal asymptote is found by dividing the coefficient on the `x`-term on the numerator by the coefficient on the `x`-term on the denominator.

Horizontal asymptote: `(x-3)/(x-2) -> x/x -> 1/1 = 1 -> y = 1`.
Vertical asymptote: `(x-3)/(x-2) -> x-2 = 0 -> x=2`.