10. How do the domains and ranges compare for the functions $y=\sqrt{x}$ and $y=\sqrt{3 x}-3 ?$
Only the domains differ.
Only the ranges differ.
Both the domains and ranges differ.
Neither the domains nor the ranges differ.

Step 1 ：The domain of a function is the set of all possible input values which will produce a valid output from a particular function. The range of a function is the set of all possible output values which will come out from the function.

Step 2 ：For the function \(y=\sqrt{x}\), the domain is all non-negative real numbers (x >= 0) because we cannot take the square root of a negative number in the real number system. The range is also all non-negative real numbers (y >= 0) because the square root of a number is always non-negative.

Step 3 ：For the function \(y=\sqrt{3x}-3\), the domain is also all non-negative real numbers (x >= 0) because we cannot take the square root of a negative number in the real number system. However, the range is all real numbers less than or equal to -3 (y <= -3) because subtracting 3 from the square root of a number will shift all the y-values down by 3 units.

Step 4 ：So, the domains of the two functions are the same, but the ranges are different.

Step 5 ：\(\boxed{\text{Only the ranges differ.}}\)