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

Jan 22, 2018

$\left[- 3 , + \infty\right) \text{ and } \left[0 , - \infty\right)$

#### Explanation:

$x + 3 \ge 0$

$\Rightarrow x \ge - 3$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ge - 3$

$\Rightarrow \left[- 3 , + \infty\right) \leftarrow \textcolor{b l u e}{\text{in interval notation}}$

$\sqrt{x + 3} \text{ has a range } \left[0 , + \infty\right)$

$\text{but "-sqrt(x+3)" is "sqrt(x+3)" reflected in the x-axis}$

$\Rightarrow \text{range is } \left[0 , - \infty\right)$
graph{-sqrt(x+3) [-10, 10, -5, 5]}