How do you find the domain and range of #f(x,y) = (x-3)^2 /4 - (y+1)^2 /16#?
Please consider the x term. Is there any real number that one can substitute into that term which would make the function be undefined. No. Therefore, x is any real number:
The y term is similar to the x term, except that is has a negative sign, therefore, the same is true for the y term:
This constitutes the domain.
For the range, please consider:
Can we do something that makes the function start from zero and approach positive infinity? Yes. We can hold y constant at -1 and let
Can we do something that makes the function start from zero and approach negative infinity? Yes. We can hold x constant at 3 and let