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

Sep 11, 2017

See below.

#### Explanation:

This is for positive roots, since $\sqrt{a}$ usually implies positive roots.

For real numbers $x + 3 \ge 0 \implies x \ge - 3$

So domain is:

$\left\{x \in \mathbb{R} | x \ge - 3\right\}$

Minimum value of range is $0$ when $x = - 3$

$\sqrt{- 3 + 3} = 0$

As $x \to \infty$

$\sqrt{x + 3} \to \infty$

so range is:

$\left\{y \in \mathbb{R} | y \ge 0\right\}$