Absolute value function

Definition

An absolute value function is a piecewise function that describes the distance of a number from zero on the number line, without considering direction. It is typically written as $f(x) = |x|$, where $|x|$ denotes the absolute value of $x$.

5 Must Know Facts For Your Next Test

1. The domain of an absolute value function is all real numbers ($\mathbb{R}$).
2. The range of an absolute value function is all non-negative real numbers ($[0, \infty)$).
3. The graph of an absolute value function forms a 'V' shape with its vertex at the origin (0,0).
4. Absolute value functions can be expressed as piecewise functions: $ f(x) = x $ if $x \geq 0$ and $ f(x) = -x $ if $x < 0$.
5. Transformations such as shifts, reflections, and stretching/compressing apply to absolute value functions similarly to other types of functions.

Review Questions

• What are the domain and range of the absolute value function?
• How does the graph of an absolute value function look?
• Express the absolute value function as a piecewise function.

Related terms

Piecewise Function: A function composed of multiple sub-functions, each defined on a specific interval within the domain.

Vertex: The highest or lowest point on the graph of an absolute value function; for $f(x) = |x|$, it is at (0,0).

Transformation: Operations that alter the graph of a function in terms of shifting, reflecting, stretching, or compressing.