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In the lecturer's notes, we say the $$\max_{i = 1,\ldots, m}(c_i^T x + d_i) $$ is a piecewise linear convex function and the notation $$\max_{i = 1,\ldots,m} $$ for the maximum value among $a_1, a_1,\ldots, a_m$

How do you sketch the graph $$y = \max(2x, 1-x, 1+x)$$ So confused right here. I can sketch the individual components, but how do I find the max of each them separately..?

Michael Hardy
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llllllllllllllllllllllllllllll
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    Draw the three curves, then the max is always the top most one at any point. For example, $|x| = \max(x,-x)$. – copper.hat Oct 08 '15 at 02:46

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From comment : Draw the three curves, then the max is always the top most one at any point. For example, $|x| = \max(x,-x)$.

Jean-François Gagnon
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  • ok I think I need to work on basics. Like So I drew |x| = max(x, -x) and I get 2 curves along the origin for y = x and y = -x. So what is top most one at any point supposed to mean here. Not sure how to use that to draw V - shaped absolute value from max. – llllllllllllllllllllllllllllll Oct 08 '15 at 03:20
  • Are you saying the very top part of the curves joining together is the max? So I would sketch the top V part of y = x and y = -x joining together? – llllllllllllllllllllllllllllll Oct 08 '15 at 03:27
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    @llllllllllllllllllllllllllllll : When you draw a graph, for each number $x$ on the $x$-axis there is a corresponding $y$-value, which in your case is the largest of $2x$, $1-x$, and $1+x$. Through the point $x$ on the $x$-axis the vertical line you see on the graph paper has three points whose $y$-coordinates are $2x$, $1-x$, and $1+x$. The one corresponding to the largest number is the highest one. ${}\qquad{}$ – Michael Hardy Oct 08 '15 at 03:47
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    @MichaelHardy Ohhh I get what you mean now. Thanks a lot for the help everyone! – llllllllllllllllllllllllllllll Oct 08 '15 at 12:56