Intercepts imply intercepting with the x-axis or y-axis.

The function would intercept the y-axis at x = 0 which is for the first piece.

It's y-intercept is at x = 0.

It's x-intercept is whenever y = 0. Notice that the x-intercept is the same as the y-intercept.

The domain is all real numbers that can go into the function. The square root cannot take any negative values and the cannot take zero, but it's not even a valid piece of the function in that region, so the domain is simply all non-negative reals. The range is just the same.