The denominator should include (x - 2)(x - 3)(x - 4) to obtain "division by 0" issues at x = 2, 3, 4.
As for the numerator, since we want a horizontal asymptote at y = 5, we need the limit of the function at infinity to equal 5. To ensure this we need a degree 3 polynomial in the numerator (that does not cancel with any of the factors in the denomintor.
==> f(x) = 5x^3 / [(x - 2)(x - 3)(x - 4)] is one such example.
(Note that lim(x→∞) f(x) = 5.)
I hope this helps!
As for the numerator, since we want a horizontal asymptote at y = 5, we need the limit of the function at infinity to equal 5. To ensure this we need a degree 3 polynomial in the numerator (that does not cancel with any of the factors in the denomintor.
==> f(x) = 5x^3 / [(x - 2)(x - 3)(x - 4)] is one such example.
(Note that lim(x→∞) f(x) = 5.)
I hope this helps!