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

1 Answer
Nov 3, 2017

Answer:

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]}