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**Sketching a graph based on certain conditions....**

Hello,

I'm supposed to sketch a graph of f based on condtions I'm given. However some of the conditions I'm given I'm not sure exactly what is supposed to happen. A little help would be greatly appreciated.

Here are the condtions, some of which I think I know what f is supposed to do, some I do not:

[itex]f'(1) = f'(-1) = 0[/itex] : Does this mean there are horizontal asymptotes at y = 1 and y = -1?

[itex]f'(x) < 0[/itex] if [itex]|x| < 1[/itex] : I believe f is decreasing here on (-1, 1)

[itex]f'(x) > 0[/itex] if [itex]1 < |x| < 2[/itex] : I believe f is increasing here on (-2, -1) and (1, 2)

[itex]f'(x) = -1[/itex] if [itex]|x| > 2[/itex] : I don't have any guesses for this one.

[itex]f''(x) < if -2 < x < 0[/itex] : I believe f is concave down on (-2, 0)

inflection point (0, 1) : I believe concavity changes at this point.

Any help would be greatly appreciated.

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