# How do you graph y=sqrtx+4, compare it to the parent graph and what is the domain and range?

Jan 26, 2018

domain is $\left\{x : x \ge 0 \mathmr{and} x \in \mathbb{R}\right\}$
range is $\textcolor{w h i t e}{\text{d.}} \left\{y : y \ge 4 \mathmr{and} y \in \mathbb{R}\right\}$
The transformation is $y = \sqrt{x}$ raised vertically by 4

#### Explanation:

You have a problem with this.

Apparently if you write $\sqrt{\text{something}}$ it is considered as representing the principle root. That is; the answer excludes the negative side of the squared values that will give $\text{something}$ when squared.

So you have the general shape of $\subset$ but only the top half of it.

Adding 4 raises that plot up the $y$ axis by 4

To avoid going into complex numbers the value being square rooted must be 0 or greater.

So we have the condition $x \ge 0$

Thus the domain is $\left\{x : x \ge 0 \mathmr{and} x \in \mathbb{R}\right\}$

When $x = 0$ we have $y = \sqrt{0} + 4 = 4$

So the range is $\left\{y : y \ge 4 \mathmr{and} y \in \mathbb{R}\right\}$

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Did you know that this is the same graph as:

$x = {\left(y - 4\right)}^{2} = {y}^{2} - 8 y + 16$

That is: a quadratic in $y$