Question

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

Answer 1

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

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.