Question

Select the correct answer.

Consider this absolute value function.

f(x)=|x - 5|



How can function f be written as a piecewise function?

Answer 1

f(x) = {5-x for x<5; x-5 for x≥5}

Explanation:

You want to write f(x) = |x -5| as a piecewise function.

Absolute value

The absolute value function is defined as ...

`|z|=\begin{cases}-z&\text{for }z < 0\\z&\text{for }z\ge0\end{cases}`

We can write your absolute value function this way by substituting (x-5) for z, and simplifying the resulting conditions.

`\boxed{f(x)=\begin{cases}5-x&\text{for }x < 5\\x-5&\text{for }x\ge5\end{cases}}`