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

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Answer 1 · 2018-07-08T06:17:32

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Given: $y = 1/2 sqrt(x + 2)$

parent function $y = sqrt(x)$

horizontal shift 2 left, horizontal stretch by 1/2

Find the domain:

The value under the radical must be $>= 0$ :

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

domain: $x >= -2 " or " [-2, oo)$

Find the range:

The range depends on the domain values. Since $x >= -2$ ,

$y = 1/2 sqrt(-2 + 2) = 0$

range: $y >= 0 " or " [0, oo)$

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

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