Write an equation for a rational function with: Vertical asymptotes at x = - 2 and x = - 3 x intercepts at x = - 4 and x = 4 y intercept at 6

[ - 9 (x^2 - 16) ] / [4 (x^2 + 5x + 6) ] = 0

Step-by-step explanation:

Ok this will be a rational function with denominator (x + 2) (x + 3) - to give the vertical asymptotes.

The numerator will be a (x + 4) (x - 4) to give the x-intercepts. The a is some constant.

As the y intercept is (0,6) we have:

6 = a (0-4) (0+4) / (0+2) (0+3)

6 = - 16a / 6

-16a = 36

a = - 36/16 = - 9/4.

So our equation is - 9 (x^2 - 16) / 4 (x^2 + 5x + 6) = 0.