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

1 Answer
Mar 5, 2018

D_f=(-\infty, 2]
Range = [0,infty)

Explanation:

Since we have a square root, the value under it cannot be negative:

2-x >=0 \implies x<= 2

Therefore, the Domain is:

D_f=(-\infty, 2]

We now construct the equation from the domain, finding the Range:

y(x\to-\infty) \to sqrt(\infty) \to \infty

y(x=2) = sqrt(2-2) = 0

Range = [0,infty)