# What is the domain and range of f(x)= sqrt(x+2) - 3??

Mar 21, 2018

$\left[- 2 , + \infty\right) , \left[- 3 , + \infty\right)$

#### Explanation:

$\text{the domain is determined by the radical}$

$\text{that is } x + 2 \ge 0 \Rightarrow x \ge - 2$

$\text{domain is "[-2,+oo)larrcolor(blue)"in interval notation}$

$f \left(- 2\right) = 0 - 3 = - 3 \Rightarrow \left(- 2 , - 3\right) \text{ is minimum}$

$\Rightarrow \text{range is } \left[- 3 , + \infty\right)$
graph{sqrt(x+2)-3 [-10, 10, -5, 5]}