Answer
Domain: $ [-3, \infty ) $
Range: $ (-\infty, 0] $
Work Step by Step
In a square root function, the sum of the numbers under the root must not be negative. In $ -\sqrt{x+3} $ , x must not be less than -3 for the sum under the root not to be negative. So the domain is $ x \geq -3 $ , also written as $ [-3, \infty ) $
The range of a square root function is $ [0, \infty) $. But because of the negative sign in $ -\sqrt{x+3} $, the range is reversed from $ [0, \infty) $ to $ (-\infty, 0] $.
