SOLUTION: I have a Calculus problem that asks me to: Find a formula for a function f that satisfies the following condition. It can not be a piecewise function. lim f(x) = 0 x→

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Question 69783: I have a Calculus problem that asks me to:
Find a formula for a function f that satisfies the following condition.
It can not be a piecewise function.
lim f(x) = 0
x→±∞
lim f(x) = -∞
x→0
f(2) = 0
lim f(x) = ∞
x→3+
lim f(x) = -∞
x→3-
So far I have:
f%28x%29=%28x%2F%28x-3%29%29-1
I'm not sure how to deal with the f(2)=0 without making it piecewise.
Any help would be greatly appreciated.
Thank you so much.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
To assure f(2)=0 you need a factor of (x-2) in the numerator.
--------
How about the following?
f(x)= (x-2)/[x(x-3)(x+3)]
Cheers,
Stan H.