Draw a graph for the function:
$y = x + | x |$

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Solution

We know that $| x | = {\begin{matrix} x f o r x \leq 0 - x f o r x < 0 \end{matrix}$
$x + | x | = {\begin{matrix} 2 x f o r x \leq 0 0 f o r x < 0 \end{matrix}$
Thus $y = {\begin{matrix} 2 x f o r x \leq 0 0 f o r x < 0 \end{matrix}$

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