Choice A is the correct answer. Test points.

1. Test (0,0): $0 > |0| - 2 \rightarrow 0 > -2$. True.
2. Test (2,0): $0 > |2| - 2 \rightarrow 0 > 0$. False.
3. Test (3,0): $0 > |3| - 2 \rightarrow 0 > 1$. False.
4. Test (0,-3): $-3 > |0| - 2 \rightarrow -3 > -2$. False.

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Choice B is incorrect (boundary).Choice C is incorrect.Choice D is incorrect.