Writing a Rational Equation Help

Question

Has to have:
-numerator is a quadratic function with a x-intercept at x=-2
-denominator is a cubic function
-there must be only one removable discontinuity at x=3
-there must be two infinite discontinuities at x=1, x=2

Answer 1

1. Root at -2 means (x+2) is a factor of the numerator
2. Removable discontinuity at 3 means that (x-3) is a factor of both the numerator and denominator
3. Infinite discontinuities at 1 and 2 mean that (x-1) and (x-2) are factors in the denominator

 

             (x+2)(x-3)
f(x) = ------------------
          (x-1)(x-2)(x-3)

 

The numerator is a quadratic, the denominator is a cubic.