SOLUTION: Write an equation for a rational function with the given characteristics. Vertical asymptotes at x = −4 and x = 8, x-intercepts at (−2, 0) and (1, 0),horizontal asymptote at y

A rational function R(x) is the ratio R(x) =   of two polynomials P(x) and Q(x).


We want the denominator Q(x) would have the zeroes at x= -4 and x= 8, giving 
vertical asymptotes.

So we take Q(x) as a quadratic function Q(x) = (x-(-4))*(x-8) = (x+4)*(x-8).



Next we want the numerator P(x) would be zero at x= -2 and x= 1, providing 
assigned x-intersectios.  So we take the numersator P(x) as a quadratic function

    P(x) = a*(x-(-2))*(x-1) = a*(x+2)*(x-1).


Now the ratio    will have the assigned x-intersections and 
assigned vertical asymptotes.


To have the given horizontal asymptote y= 2 at x -- +/- ,  we take a = -2.


So, finally our rational function is  R(x) = .    ANSWER