What is the domain and range of $f(x,y)=x^4/(x^4 + y^2)$? I believe the domain is:
x,y cannot equal to 0 OR x can be any real number but y cannot equal to 0 
and the range, well I just have no approach in solving it. Are just supposed to know because it's a rational function? or is there a proper approach in finding the range? I know that the function is always positive due to the terms having squares, so it must be greater than 0, but how do we find the end limit?

For the domain note that
$$
x^4 + y^2=0\iff(x,y)=(0,0).
$$
Hence the domain is $\mathbb{R}^2\setminus \{(0,0)\}$.
