Question

Express f(x) = |x| as a piecewise function.

Answer 1

The function f(x) = |x| uses the operator called "module" (the vertical bars), and what this operator does is the result will always be a positive number.

So, for example, the module of 3 is equal 3, and the module of -5 is equal 5.

The result is just the same number, but always positive.

So as we have a variable inside the bars, we have the module of x.

This means that if x is a positive number (x >= 0), the result will be x.

But if x is a negative number (x < 0), the result will be -x (because -x will be a positive number).

Then, expressing this as a piecewise function, we have:

`\begin{gathered} f(x)=|x| \\ f(x)=\left\{ \begin{aligned}x,\text{ if }x\ge0 \\ -x,\text{ if }x<0\end{aligned}\right. \end{gathered}`