Graph of root of quadratic function This is a problem new to me. I need some guidance on what I should study/understand to be able to solve such problems.

Sketch the graph of the following absolute functions on $\mathbb{R}$ and state the range.
  $$g:x \rightarrow \sqrt {x^2 + 2}$$

I have done graphs of quadratic equations and square root functions. How do I do a graph of root function of a quadratic function?
Thanks for your help.
Edit: Clarified question.
I have tried plotting points. I got a curve that resembles the parabolic curve of a quadratic function. The quadratic function has a vertex formula, is open/closed parabola, etc.

I was wondering if there were any thing I need to study on the lines of the quadratic function? What if it is the nth root. Is there a way to figure this out for (fractional)powers of a quadratic?

The other approach I was looking at was via graph transformations.
$$g(x) = \sqrt{x^2 + 2}$$
Let, $$h(x) = \sqrt{x}$$
Then, $$g(x) = h(x^2 + 2)$$
I not sure where to go further with this idea.
 A: It sort of depends on how detailed a graph you want.  Note first of all that the graph is symmetrical about the $y$-axis.  This observation immediately cuts our work in half! Just do the graph for $x$ positive, and reflect the picture across the $y$-axis.
So we take $x \ge 0$.  Near $x=0$, we have that $y \approx \sqrt{2}$.  As $x$ increases, $\sqrt{x^2+2}$ increases.  
For $x$ at all large positive, we have that $\sqrt{x^2+2}\approx x$.  More precisely, it is a little bigger than $x$, but awfully close to $x$ when $x$ is large. (You may want to do a small number of calculations, using a calculator.)
Draw the half-line $y=x$, for $x \ge 0$.  To say that $\sqrt{x^2+2}$ is awfully close to $x$, when $x$ is large, means that the curve $y=\sqrt{x^2+2}$ hugs the half-line $y=x$, for $x \ge 0$, when $x$ is large.  So for large values, your curve will be roughly indistinguishable from $y=x$.
In technical language, the half-line is an (oblique) asymptote to the curve $y=\sqrt{x^2+2}$.
With this information, you should be able to get a good idea of the first-quadrant part of the curve.  Then don't forget to reflect across the $y$-axis.
Wish I could supply a picture.  There are (free) graphing calculator programs, or more generally graphing programs, available for download.
Look up also Wolfram Alpha.  It will draw the curve for you.  But first do it yourself.
A: I realize you've accepted an answer.  I just thought it might be helpful if you were to compare the equations:
$$y = \sqrt{x^2 + 2}$$
with
$$y^2 = x^2 + 2 \quad\iff\quad y^2 - x^2 = 2$$ 
and their corresponding graphs.  Do you see a relationship? 

They are certainly related, but the range of the first equation (the graph of which is  entirely above the $x$-axis, since $y\geq 2$ for all $y$) is half that of the first equation (entire graph of hyperbola includes both the negative and positive values in the range $y$).
I encourage you to explore with graphing the equations at WolframAlpha.
Have you studied conic sections or worked with graphs of conics such as parabolas, hyperbolas, ellipses and circles?  If not, you might want to check out Wikipedia on Conic Sections for a sneak preview of what's to come!
