Absolute value

Definition

Absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative number.

5 Must Know Facts For Your Next Test

1. The absolute value of a number $x$ is denoted as $|x|$.
2. $|x| = x$ if $x \geq 0$, and $|x| = -x$ if $x < 0$.
3. Absolute value functions are V-shaped when graphed in a coordinate plane.
4. The domain of the absolute value function $f(x) = |x|$ is all real numbers, and the range is all non-negative real numbers ($[0, \infty)$).
5. Equations involving absolute values can have two solutions, corresponding to both positive and negative scenarios.

Review Questions

• What is the absolute value of -7?
• What does the graph of an absolute value function look like?
• If $f(x) = |x+3|$, what are the domain and range of this function?

Related terms

Domain: The set of all possible input values (typically $x$-values) for which a function is defined.

Range: The set of all possible output values (typically $y$-values) that a function can produce.

Piecewise Function: A function composed of multiple sub-functions, each defined over a specific interval.