The $\textrm{abs}$ function is used when you need to get the size of a number and you don't care if the number is positive or negative. The absolute value just ignores the sign of a number.

$$f(x)=|x|= x \text{ if } x>0 \text{ or } -x \text{ if } x<0$$

• Always returns a non-negative number.
• The combination of squaring followed by square-root is equivalent

to the absolute value function:

  \[
    \sqrt{ x^2 }  \equiv |x|.
  \]