Try another similar question reattempt last question below o

Try another similar question, reattempt last question below, or select another q Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 2 x intercepts at x = 5 and x = 3 Horizontal asymptote at y = 3

Solution

vertical asymptotes at x =-4 , x =2 => denominator of function contain (x+4)(x-2)

x intercept at x =5 ,x=3 => numerator has (x-5)(x-3)

let function be y =k((x-5)(x-3))/((x+4)(x-2))

given horizontal asymptote at y =3

horizontal asymptote y =lim_x->infinityk((x-5)(x-3))/((x+4)(x-2)) =3

lim_x->infinityk(x²(1- 5/x)(1 -3/x))/(x²(1 +4/x)(1 -2/x)) =3

lim_x->infinityk((1- 5/x)(1 -3/x))/((1 +4/x)(1 -2/x)) =3

k((1- 0)(1 -0))/((1 +0)(1 -0)) =3

k=3

function is  y =3((x-5)(x-3))/((x+4)(x-2))