Question

Write an equation for a rational function with: Vertical asymptotes at x = -1 and x = 3 x intercepts at x = -2 and x = -6 Horizontal asymptote at y = 7 y =

Answer 1

Answer:

$\frac{7(x+2)(x+6)}{(x+1)(x-3)}$

Step-by-step explanation:

The vertical asymptotes need to be in the denominator. They become VA's when that small expression value equals zero.

x=-2 will become (x+2)

and x=-6 will become (x+6)

The x intercepts will be in the numerator.

x=-1 will go with (x+1) and x=3 will go with (x-3)

The horizontal A must be the quotient of the coefficient of the numerator and denominator, since both the top and bottom have the same power.

To make the quotient 7, we place a seven in the numerator so 7/1=7.