Write a function that has a horizontal asymptote at y = 4 and vertical asymptotes at x = - 2 and x = -6.

Question

Hi I'm a Sophomore in Highschool who was hoping to get some help on this problem I'm stuck on

Answer 1

The vertical asymptotes mean that we have x+2 and x+6 as factors in the denominator. To have a horizontal asymptote of 4, the numerator and denominator have to have the same degree, and the leading coefficients of the numerator divided by the leading coefficient of the denominator must be 4.

The obvious polynomial fraction to use is

4x^2/((x+2)(x+6)) or 4x^2/(x^2+8x+12)