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!

You're welcome! I'm glad I could help explain it to you. In the equation y=x^2, when you square any real number x, the result is always positive because a negative number squared becomes positive. Therefore, y can never be a negative number, which means the range (the set of all possible y values) is all non-negative numbers (y is greater than or equal to 0).

Similarly, in the equation x=y^2, no matter what y value you choose, once it is squared, the result will always be positive. This means x can only be a non-negative number.

In general, the domain is the set of all possible x values that you can choose and the range is the set of all possible y values that can be obtained from those x values in the equation.

If you have any more questions, feel free to ask!