What is domain and range of f(x,y)=e^-(x²+y²)

Question

Domain and range of the several variable

Answer 1

Regardless of what x and y may be, the exponent is either 0 or some negative number. Therefore the range of z=f(x,y) is bounded by 1 (upper bound) and the other z values can get to very small but never as little as zero.

 

Domain: x any Real, y any Real

Range (0,1]