How do you find the domain and range of y =sqrt(2 - x)?

1 Answer
Nov 3, 2017

Domain is x<=2, x in R , range is y>=0, y in R.

Explanation:

If we are dealing with real numbers, we cannot include any values of x in the domain which will render the value of 2-x as negative, hence domain is restricted to x<=2, x in R.
The radical symbol sqrt returns only the positive square root of the bracket and so the range is restricted to y>=0, y in R.
A graph helps to see both of these:
graph{sqrt(2-x) [-10, 10, -5, 5]}