Write an equation for a rational function with the given characteristics

Question

Vertical asymptotes at x=−1 and x=3

x-intercepts at (−4,0) and (2,0)

horizontal asymptote at y=−2

Answer 1

x=-4, x =2 are x intercepts, the points (-4,0), (2,0)

corresponding factors are (x+4)(x-2)

vertical asymptotes -1 and 3 mean those values make the denominator = 0

such as (x+1) and (x-3)

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

horizontal asymptote is y=-2 = a

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

y = -2(x^2 -4x -8)/(x^2 -2x -3)

y = (-2x^2 +8x +16)/(x^2 -2x -3)

Answer 2

Hope this helps! Not enough time to fully explain some of these concepts, so please let me know if you need to clarify these points.