# What are the domain and range of y= 1+sqrt(x+3)?

Jan 13, 2018

Domain: $\left[- 3 , + \infty\right)$ Range:$\left[1 , + \infty\right)$

#### Explanation:

$y = 1 + \sqrt{x + 3}$

$y$ is defined where $x + 3 \ge 0 \to x \ge - 3$

Hence, the domain of $y$ is $\left[- 3 , + \infty\right)$

$y$ has a minimum value of 1 where $x = - 3$

$y$ has no finite upper bound.

Hence, the range of $y$ is $\left[1 , + \infty\right)$

We can deduce these results from the graph of $y$ below.

graph{1+sqrt(x+3) [-10, 10, -5, 5]}