What is the restricted domain along with the X and Y intercepts for the equation y equals square root of x?

The domain of y = x0.5 is [0,+Infinity]. There are no X and Y intercepts for this function.

Not asked, but answered for completeness sake, the range is also [0,+Infinity]. That is why there are no intercepts.

Taken one step further, if you include the domain [-Infinity,0) in your analysis, you must include the imaginary range (i0,iInfinity] in your result set.