Question

How do you find the domain and range of `y = sqrt(x-3)`?

Answer 1

domain: all real numbers x such that `x >= 3`
range: all real numbers y such that y >= 0#

Explanation:

The domain of a function is all the values of x for which the function is defined.

For `y = sqrt(x - 3)`, this is all numbers x such that `x >= 3`, since any value of x less than 3 would result in having to find the square root of a negative number. (we're ignoring complex numbers here.).

The range of the function is all the output values that could be produced by the function.

With a big enough positive input value x, you could produce any positive output number y. (You could also produce y = 0 when x = 3).

Therefore, the range of this function is all real numbers greater than zero.

...always helps to have a graph of the function as a sanity check:
graph{sqrt(x - 3) [-10, 10, -5, 5]}