Question

how come in y=x^2, the range is all real numbers, y is greater than or equal to 0

or is it for x=y^2?

in y=x^2 imagine any choice of x (the domain) you might make.
No matter what x you choose, once you square it, it becomes positve.
So y can never be a negative number, therefore the range can be any non-negative number.

On the other hand for x = y^2
no matter what y you choose, once it is squared the result would be positive, thus the x can only be a non-negative number.

generally speaking, the domain is your choice of x's, and the range is your choice of y's that you can make in your equations.

thank you sooooooooo much!