# How do you find the domain and range for y= (x+3)^0.5?

May 29, 2018

Domain: $\left\{x | x \ge - 3\right\}$ or $\left[- 3 , \infty\right)$

Range: $\left\{y | y \ge 0\right\}$ or $\left[0 , \infty\right)$

#### Explanation:

$y = {\left(x + 3\right)}^{0.5}$

$y = {\left(x + 3\right)}^{\frac{1}{2}}$

$y = \sqrt{x + 3}$

So the domain will be all numbers where the terms under the radical are not negative (otherwise the solution is imaginary).

$x + 3 \ge 0$

$x \ge - 3$

Domain: $\left\{x | x \ge - 3\right\}$ or $\left[- 3 , \infty\right)$

Now the range at x=-3; y=0 but it will always be greater than or equal to 0.

Range: $\left\{y | y \ge 0\right\}$ or $\left[0 , \infty\right)$

Here is the graph:

graph{sqrt(x+3) [-6, 14, -1.28, 8.72]}