Absolute value functions

Definition

Absolute value functions are mathematical functions that describe the distance of a number from zero on the number line, regardless of direction. They are denoted as $f(x) = |x|$ and produce non-negative outputs.

5 Must Know Facts For Your Next Test

1. The graph of an absolute value function, $f(x) = |x|$, is a V-shape with its vertex at the origin (0,0).
2. Absolute value functions can be written as piecewise functions: $f(x) = x$ if $x \geq 0$ and $f(x) = -x$ if $x < 0$.
3. The domain of absolute value functions is all real numbers, while the range is all non-negative real numbers.
4. Vertical shifts in absolute value functions can be represented as $f(x) = |x| + c$, where $c$ moves the graph up or down.
5. Horizontal shifts in absolute value functions are represented as $f(x) = |x - h|$, where $h$ moves the graph left or right.

Review Questions

• What does the graph of an absolute value function look like?
• How can you express an absolute value function as a piecewise function?
• What are the domain and range of an absolute value function?

Related terms

Piecewise Functions: Functions that have different expressions based on different intervals of their domain.

Vertex: The highest or lowest point on the graph of a parabola or absolute value function.

Transformation: Operations that alter the form of a figure, such as translations, reflections, stretches, and compressions.