Question

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

Answer 1

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]}