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If you are talking about functions in 2-dimensional space, that is, functions of the sort y = f(x), then, by definition, none can be positive in the third quadrant where y is always negative.

If you are talking about functions in 3-dimensional space, ie functions of the kind z = f(x,y), then for the third quadrant in terms of x and y (x<0 and y<0), there are infinitely many functions for which z > 0.

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Q: What functions are positive in the third quadrant?
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