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?

A. f(x) = (-3(x-4)(x+2))/(x²-1)
B. f(x) = (x²-1)/(-3(x+4)(x-2))
C. f(x) = (x²-1)/(-3(x+4)(x+2))
D. f(x) = (-3(x+4)(x+2))/(x²-1)

Answer 1

The equation that describes a rational function with specified intercepts and asymptotes is A. f(x) = (-3(x-4)(x+2))/(x²-1).

Step-by-step explanation:

The equation that 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 is A. f(x) = (-3(x-4)(x+2))/(x²-1).

To determine this, we can observe that the x-intercepts are the values of x where the numerator equals 0, and the vertical asymptotes are the values of x where the denominator equals 0. Additionally, the horizontal asymptote is found by comparing the degrees of the numerator and denominator. In this case, the degrees are equal, so the horizontal asymptote is y = the ratio of the leading coefficients, which is -3.

Using these observations, we can see that option A satisfies all the given criteria.