# How do you write y = -2|x-4|+4 as a piecewise function?

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#### Explanation

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#### Explanation:

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May 26, 2018

The piecewise function is $y = \left\{\begin{matrix}- 2 x + 12 \mathmr{if} x \ge 4 \\ 2 x - 4 \mathmr{if} x < 4\end{matrix}\right.$

#### Explanation:

The function is

$y = - 2 | x - 4 | + 4$

$x - 4 \ge 0$, $\implies$, $x \ge 4$

Therefore,

$y = - 2 | x - 4 | + 4 = \left\{\begin{matrix}- 2 \left(x - 4\right) + 4 \mathmr{if} x \ge 4 \\ - 2 \left(- \left(x - 4\right)\right) + 4 \mathmr{if} x < 4\end{matrix}\right.$

$y = \left\{\begin{matrix}- 2 x + 12 \mathmr{if} x \ge 4 \\ 2 x - 4 \mathmr{if} x < 4\end{matrix}\right.$

graph{-2|x-4|+4 [-10, 10, -5, 5]}

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