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

Apr 25, 2017

$\text{domain } x \in \mathbb{R} , x \ge 2$
$\text{range } y \in \mathbb{R} , y \ge 0$

#### Explanation:

For real numbers the root cannot be negative.

$\Rightarrow x - 2 \ge 0 \Rightarrow x \ge 2$

$\Rightarrow \text{domain is } x \in \mathbb{R} , x \ge 2$

$\text{hence } y \ge 0$

$\Rightarrow \text{range is } y \in \mathbb{R} , y \ge 0$
graph{3sqrt(x-2) [-10, 10, -5, 5]}