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Sketch the graph of the function.

$ f(x) = x + | x | $

$|x|=\left\{\begin{array}{ll}x & \text { if } x \geq 0 \\ -x & \text { if } x<0\end{array}\right.$

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

Graph the line $y=2 x$ for $x \geq 0$ and graph $y=0$ (the $x$ -axis) for $x<0$

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Johns Hopkins University

Harvey Mudd College

University of Nottingham

Boston College

he sketched the graft the functions So we have F equals X plus the absolute value of ax. And to start off we'LL start with the definition here for the absolute value of X equals positive X. If X is greater than equal, did it greater than or equal to zero and negative acts if excess less than her uh, X is less than zero. So if you're not convinced that this just take a moment and pause. Teo, convince yourself that this is true. Hey, and so f in this case is going to be either X plus X if X is greater than or equal to zero or it's going to be X minus sechs. Yeah, ex lesson tio continuing on Well, we get into getting two acts Yes, X rated R zero or it's going to be zero. Otherwise so to graft this So two X if X is greater than or equal to zero So well, I include zero here with, uh, two acts like that, and zero otherwise So I have school. Axe is legal. Wait, Did this graph dysfunction