Question 1168760
needs (x-3)/(x-3) for the discontinuity.
(x-1)(x-2) in the numerator for the roots
(x-4) in the denominator for the asymptote
3 in the numerator and another term with x in the denominator so that the power of the numerator and denominator are both the same to give the asymptote of 3. I used (x-4), since it did not affect the roots or the hole.

3(x-1)(x-2)(x-3)/(x-3)(x-4)^2

{{{graph(300,300,-3,4,-10,10,3(x-1)(x-3)(x-2)/(x-3)(x-4)^2)}}}

{{{graph(300,300,-5,100,-10,10,3(x-1)(x-3)(x-2)/(x-3)(x-4)^2)}}}