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

##### 1 Answer

domain: all real numbers x such that

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

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]}