# What is the domain and range of x =(y+2)^2?

Feb 15, 2017

Domain: $\left[0 , \infty\right)$, Range: $\left[- 2 , \infty\right)$

#### Explanation:

To graph, you need to solve for $y$:

Square root both sides: $\sqrt{x} = y + 2$
Isolate the variable $y$: $y = \sqrt{x} - 2$

Analytically finding the domain:
$\sqrt{x} \ge 0$ which means $x \ge 0$

If $x \ge 0$ then $y \ge - 2$

From the graph: graph{sqrt(x) - 2 [-10, 10, -5, 5]}