# How do you graph y=1/2sqrt(x+2), compare to the parent graph, and state the domain and range?

Jul 8, 2018

#### Explanation:

Given: $y = \frac{1}{2} \sqrt{x + 2}$

parent function $y = \sqrt{x}$

horizontal shift 2 left, horizontal stretch by 1/2

Find the domain:

The value under the radical must be $\ge 0$:

x + 2 >= 0; " "x >= -2

domain: $x \ge - 2 \text{ or } \left[- 2 , \infty\right)$

Find the range:

The range depends on the domain values. Since $x \ge - 2$,

$y = \frac{1}{2} \sqrt{- 2 + 2} = 0$

range: $y \ge 0 \text{ or } \left[0 , \infty\right)$

graph{1/2 sqrt(x + 2) [-10, 10, -5, 5]}