Absolute value

Definition

Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is always non-negative and is denoted by vertical bars, e.g., $|x|$.

5 Must Know Facts For Your Next Test

1. The absolute value function is defined as $|x| = x$ if $x \geq 0$ and $|x| = -x$ if $x < 0$.
2. The graph of an absolute value function forms a 'V' shape.
3. Absolute value equations can have two possible solutions: positive and negative scenarios.
4. The domain of an absolute value function is all real numbers ($ \mathbb{R} $).
5. The range of an absolute value function is all non-negative real numbers ($ y \geq 0 $).

Review Questions

• What does the graph of an absolute value function look like?
• How do you solve the equation $ |x - 3| = 7 $? Provide both possible solutions.
• What are the domain and range of the absolute value function $ f(x) = |2x - 5| $?

Related terms

Domain:

The set of all possible input values (usually represented as $ x $) for which a function is defined.

Range:

The set of all possible output values (usually represented as $ y $) that a function can produce.

Piecewise Function:

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