How do you write 2 |x-2| +5 as a piecewise function?

Aug 17, 2017

$f \left(x\right) = - 2 x + 9 | x < 2$
$f \left(x\right) = 2 x + 1 | x \ge 2$

Explanation:

$f \left(x\right) = 2 \left\mid x - 2 \right\mid + 5$ , Critical point is $x - 2 = 0 \mathmr{and} x = 2$

Written as piecewise function,

$f \left(x\right) = - 2 \left(x - 2\right) + 5 | x < 2$
$f \left(x\right) = 2 \left(x - 2\right) + 5 | x \ge 2$

OR

$f \left(x\right) = - 2 x + 9 | x < 2$
$f \left(x\right) = 2 x + 1 | x \ge 2$ [Ans]