Question

For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1?

f (x) = StartFraction 2 x Superscript m Baseline Over x + a EndFraction
a = –1, m = 0
a = 1, m = 0
a = –1, m = 1
a = 1, m = 1

Answer 1

We need x + a = 0 at x = 1, so a = −1. For a horizontal asymptote y = 2, the degrees of numerator and denominator must be equal so the ratio of leading coefficients is 2:1, hence m = 1.

Thus a = −1, m = 1.