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Finding a Function that Satisfies a Limit

Find a formula for a function f, that satisfies the following conditions:
1. lim(x->+/-infinity)f(x) = 0,
2. lim(x->0)f(x) = -infinity,
3. lim(x->3-)f(x) = infinity,
4. lim(x->3+)f(x) = -infinity,
5. f(2) = 0.

Solution Summary

Functions are found that satisfy limits. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.