What is the domain of the function y = sqrt(x)?

The domain of the function \( y = \sqrt{x} \) is \( x \geq 0 \).

In more detail, the domain of a function is the set of all possible input values (x-values) that will produce a valid output. For the function \( y = \sqrt{x} \), we need to consider when the square root is defined. The square root of a number is only defined for non-negative numbers, meaning \( x \) must be greater than or equal to zero. If \( x \) is negative, the square root is not a real number, and thus not valid in this context.

To put it simply, you can input any non-negative number into the function \( y = \sqrt{x} \) and get a real number as the output. For example, if \( x = 0 \), then \( y = \sqrt{0} = 0 \). If \( x = 4 \), then \( y = \sqrt{4} = 2 \). However, if you try to input a negative number, like \( x = -1 \), the function \( y = \sqrt{-1} \) does not produce a real number, so it is not included in the domain.

In summary, the domain of \( y = \sqrt{x} \) includes all non-negative numbers, which can be written in interval notation as \( [0, \infty) \). This means you can use any value from 0 to positive infinity as an input for \( x \).