Write an equation for a rational function with vertical asymptote at x=-1 and x=2 x inter at x=-3 and x=-6 horizontal asymptote at y=3

Question

Write an equation for a rational function with

vertical asymptote at x=-1 and x=2

x inter at x=-3 and x=-6

horizontal asymptote at y=3

Answer 1

Each of these characteristics corresponds to a specific part of the the rational function. If x=a is a vertical asymptote, then (x-a) must be a factor in the denominator. If x=b is an intersect, then (x-b) must be a factor in the numerator. If y=c is the horizontal asymptote then when you divide the leading terms you should get c. For instance if I had a function with a vertical asymptote at x=4, an intersect at x=-2, and a horizontal asymptote of y=8 then my rational function could be f(x)=8(x+2)/(x-4).