What are the asymptotes of the graph of f(x) ?

When in doubt, graph it.

The 3rd and 4th choices are appropriate.

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This is what is known as a "logistic function." It is used to model population growth when there is a resource limit. It starts out exponential, but then slows as it reaches the "carrying capacity" of the environment. The lower asymptote is zero; the upper one is the carrying capacity of the resource--here 15/1 = 15.