# How do you find the domain and range of y=sqrt(3-x)?

Jan 29, 2017

Domain : $x \in \left(- \infty , 3\right]$
Range : $y \in \left[0 , \infty\right)$
See the illustrative semi-parabola graph.

#### Explanation:

$y = \sqrt{x - 3} \ge 0$

For y to be real, $x \le 3$

graph{sqrt(3-x) [-10, 10, -5, 5]}