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

Question

y=

Answer 1

Vertical asymptotes give linear factors in the denominator of (x-3) (x+2)

x intercepts give linear factors in the numerator of (x+3) (x-4)

So y = a (x-3)(x+2) / (x+3) (x-4)

when x=0, y = a (-3)(2)/(3) (-4) = 1/2 a

We need y intecept at 4, so 1/2a = 4, so a=8

So function is y = 8 (x-3) (x-2) / (x+3) (x-4)