absolute value

The absolute value of a number \( x \) is its distance from zero on the number line, regardless of its sign, and it is denoted by \( |x| \).

Absolute value equations are equations in which the variable \( x \) appears inside an absolute value expression.

Inequalities with absolute value are inequalities in which an expression of the form \( |f(x)|\) appears.

Function transformations are operations that change a function’s graph through translations, reflections, scaling, and absolute value operations.

The absolute value function assigns to each real number its distance from zero on the number line:

\[
y = |x| =
\begin{cases}
+x & \text{if } x \geq 0 \\[0.5em]
-x & \text{if } x < 0 \end{cases} \]