Absolute value function

Definition

An absolute value function is a type of piecewise function that returns the non-negative value of its input. It is denoted as $f(x) = |x|$ and has a V-shaped graph.

5 Must Know Facts For Your Next Test

1. The domain of an absolute value function is all real numbers, $(-\infty, \infty)$.
2. The range of an absolute value function is all non-negative real numbers, $[0, \infty)$.
3. The vertex of the graph of an absolute value function $f(x) = |x|$ is at the origin (0,0).
4. An absolute value function can be written as a piecewise function: $f(x) = x$ if $x \geq 0$, and $f(x) = -x$ if $x < 0$.
5. Absolute value functions are always symmetric with respect to the y-axis.

Review Questions

• What is the domain and range of the absolute value function?
• How can you express the absolute value function as a piecewise function?
• Where is the vertex located on the graph of an absolute value function?

Related terms

Piecewise Function: A function composed of multiple sub-functions, each applying to a certain interval of the main function's domain.

Vertex: The highest or lowest point on the graph of a parabola or other curve; for an absolute value function, it is where the two linear pieces meet.

Symmetry: \text{A property where one half of a shape or figure is a mirror image of its other half. Absolute value functions exhibit symmetry with respect to the y-axis.}