sketching the graph of functions

Question

Good morning!

How to draw the graph of the following function and discuss the increasing and decreasing intervals of y.

$y = $x$ + \sqrt[]{x^2}$

Also, I would like to know free online graphing calculator

Thanks in advance.

Answer 1

Hint: Recall that $\sqrt{x^2} = |x|$, so

$$f(x) = x + |x| = \left\{\begin{array}{lr} 2x &: \text{ if } x \ge 0 \\ 0 &: \text{ if } x < 0 \end{array}\right.$$

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For an online graphic calculator, I would suggest Wolfram Alpha.