Question

Determine the horizontal asymptote for r(x) = x^3-2x^2+3 / x-2, if one exists.

A) There is no horizontal asymptote.
B) The horizontal asymptote is y = 0.
C) The horizontal asymptote is x = 2.
D) The horizontal asymptote is y = x - 1.

Answer 1

There is no horizontal asymptote.

Answer 2

Explanation:

A horizontal asymptote exists for this function at y = 0.

Compare the degrees of the numerator and denominator

If N < D, then y = 0 is the horizontal asymptote.

If N = D, then y =

a

b

(a = leading coefficient numerator and b = leading coefficient denominator).

If N > D, then there is no horizontal asymptote.

If N > D by only one, then there is a slant asymptote.