# How do you write f(x)= |x+9| as a piecewise function?

Jun 24, 2017

See explanation.

#### Explanation:

To write this function as a piecewise function you have to use the definition of absolute value.

The definition says that:

## $| x | = \left\{\begin{matrix}x & x \ge 0 \\ - x & x < 0\end{matrix}\right.$

Applying this definition to your function you get:

$| x + 9 | = \left\{\begin{matrix}x + 9 & x + 9 \ge 0 \\ - x - 9 & x + 9 < 0\end{matrix}\right.$

After simplifying the inequalities you get:

$| x + 9 | = \left\{\begin{matrix}x + 9 & x \ge - 9 \\ - x - 9 & x < - 9\end{matrix}\right.$

So finally you can write the function as:

$f \left(x\right) = \left\{\begin{matrix}x + 9 & x \ge - 9 \\ - x - 9 & x < - 9\end{matrix}\right.$