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.