# How do you write f(x) = |2x+3| as a piecewise function?

Feb 11, 2018

Use the definition:
$| f \left(x\right) | = \left\{\begin{matrix}f \left(x\right) \text{ & "f(x) >= 0 \\ -f(x)" & } f \left(x\right) < 0\end{matrix}\right.$

#### Explanation:

Given $f \left(x\right) = | 2 x + 3 |$

Using the definition:

$f \left(x\right) = | 2 x + 3 | = \left\{\begin{matrix}2 x + 3 \text{ & "2x+3 >= 0 \\ -2x-3" & } 2 x + 3 < 0\end{matrix}\right.$

It is good practice to simplify the inequalities:

$f \left(x\right) = \left\{\begin{matrix}2 x + 3 \text{ & "2x >= -3 \\ -2x-3" & } 2 x < - 3\end{matrix}\right.$

Finished:

$f \left(x\right) = \left\{\begin{matrix}2 x + 3 \text{ & "x >= -3/2 \\ -2x-3" & } x < - \frac{3}{2}\end{matrix}\right.$