find the formula that satisfies the following conditions?

Question

lim f(x) = 0 when x approach to + - infinity, lim f(x) = - infinity when x approach to 0, f(2) = 0, lim f(x) = infinity when x approach to 3- , lim f(x) = - infinity when x approach to 3+

Answer 1

is the lim f(x) = -infinity when x approaches 0+ and from 0- as well?

I have found
y = (x-2)/(-x^2+3x) to be close, but lim f(x) = + infinity when x approaches 0-

Answer 2

-(x-2)^2(1-1/(x+3)^12+1/(x-3)^12) It works.

Answer 3

f(x)=lnIxI*(x-2)/(3-x)IxI