I found it on an exam and it stumped me. Is it considered a function? Because I get the same outputs from $x = 0$; and $x = 1/2$
2026-03-27 04:34:26.1774586066
How to graph $x|2x-1|-3$?
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Since $|a|$ equals $a$ for $a \geq 0$, and $-a$ otherwise, we just have two cases to look at depending on what happens to the expression inside the absolute value, $2x-1$. We have that $$x|2x-1|-3 = \begin{cases} x(2x-1)-3 = 2x^2-x-3, &\mbox{ if }x\geq 1/2, \\ -x(2x-1)-3 = -2x^2+x-3, &\mbox{ if } x<1/2.\end{cases}$$Can you graph both parabolas and paste them together suitably?