Question

Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?

f(x) =
f(x) =
f(x) =
f(x) =

Answer 1

One suitable function is

f(x) = -3(x + 4)(x - 2) / ((x - 1)(x + 1)).

Explanation: zeros at x = -4, 2 from the numerator; vertical asymptotes at x = ±1 from the denominator (no cancellations); degrees are equal and the ratio of leading coefficients is -3, so the horizontal asymptote is y = -3.