Interval notation

Definition

Interval notation is a mathematical notation used to describe sets of numbers lying within a specific range. It uses brackets and parentheses to denote inclusive and exclusive bounds, respectively.

5 Must Know Facts For Your Next Test

1. Square brackets $[a, b]$ indicate that both endpoints $a$ and $b$ are included in the interval.
2. Parentheses $(a, b)$ indicate that both endpoints $a$ and $b$ are excluded from the interval.
3. A combination such as $[a, b)$ means that $a$ is included but $b$ is excluded.
4. $(-\infty, b)$ or $(a, \infty)$ can be used to represent intervals extending infinitely in one direction.
5. Interval notation can describe the domain and range of functions effectively.

Review Questions

• What does the interval notation $(3, 7]$ signify?
• How do you represent all real numbers greater than or equal to 5 using interval notation?
• Convert the inequality $2 < x \leq 6$ into interval notation.

Related terms

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

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

Inequality: A mathematical statement indicating that two expressions are not equal and have a greater-than or less-than relationship.