Question

Write an equation for a rational function with:

Vertical asymptotes at x = -2 and x = 6

x intercepts at x = -5 and x = 5

Horizontal asymptote at y = 2
please help!

Answer 1

Hi,

Explanation:

Vertical asymptotes at x = -2 and x = 6 => y=P(x)/((x+2)(x-6)

x intercepts at x = -5 and x = 5 => P(x)=k*(x+5)(x-5)

Horizontal asymptote at y = 2

`\displaystyle \lim_(n \to \infty) (k*(x+5)(x-5))/((x+2)(x-6)) =2\\\\\Longrightarrow\ k=2\\`