Write a function with vertical asymptotes at x=2, x=3, and x=4 and horizontal asymptote at y=5
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Write a function with vertical asymptotes at x=2, x=3, and x=4 and horizontal asymptote at y=5

[From: ] [author: ] [Date: 11-05-12] [Hit: ]
(Note that lim(x→∞) f(x) = 5.I hope this helps!......
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!
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