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

Mar 5, 2018

${D}_{f} = \left(- \setminus \infty , 2\right]$
Range $= \left[0 , \infty\right)$

#### Explanation:

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

$2 - x \ge 0 \setminus \implies x \le 2$

Therefore, the Domain is:

${D}_{f} = \left(- \setminus \infty , 2\right]$

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

$y \left(x \setminus \to - \setminus \infty\right) \setminus \to \sqrt{\setminus \infty} \setminus \to \setminus \infty$

$y \left(x = 2\right) = \sqrt{2 - 2} = 0$

Range $= \left[0 , \infty\right)$