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I'm not sure about how solid this reasoning is, but I sort of based my answer on how I know $e^{-x^2}$ behaves. If you remember from quantum mechanics, this type of function has a high value at one spot and a low value everywhere else; adding $y^2$ to the exponent should only extend this to another dimension. Plot II looks like it peaks in one spot and is small everywhere else, so I would pick it to be the plot of $e^{-(x^2+y^2)}$.

I'm not sure about how solid this reasoning is, but I sort of based my answer on how I know $e^{-x^2}$ behaves. If you remember from quantum mechanics, this type of function has a high value at one spot and a low value everywhere else; adding $y^2$ to the exponent should only extend this to another dimension. Plot II looks like it peaks in one spot and is small everywhere else, so I would pick it to be the plot of $e^{-(x^2+y^2)}$.

I'm not sure about how solid this reasoning is, but I sort of based my answer on how I know $e^{-x^2}$ behaves. If you remember from quantum mechanics, this This type of function has a high value at one spot and a low value everywhere else; adding $y^2$ to the exponent should only extend this to another dimension. Plot II looks like it peaks in one spot and is small everywhere else, so I would pick it to be the plot of $e^{-(x^2+y^2)}$.

In general I sort of expect $e^{-(junk)^2}$ to behave like this since we use these functions so often to represent peak values in one area with minimal values in others. I've also noticed that on our sheets, a lot of the plots that look like isolated hills and holes are complicated combinations and variations of this type of function.