Unit One: Patterns, Relations, and the Cartesian Coordinate System

Vocabulary practice flashcards covering Unit One notes on patterns (arithmetic and geometric), the Cartesian coordinate system, relations, Cartesian products, and domains and ranges.

Pattern

A regular, repeated, recurring form or design used for identifying relationships and finding logic in order to form generalizations and make predictions.

Arithmetic Pattern

A classification of pattern—also known as an algebraic pattern—where the sequence of numbers is determined by addition and subtraction operations.

Geometric Pattern

A classification of pattern where the sequence of numbers is determined by multiplication and division operations.

Cartesian Coordinate System

A two-dimensional system consisting of two perpendicular lines: a horizontal line and a vertical line.

Abscissa

The horizontal line or $x$-axis in a rectangular Cartesian coordinate system.

Ordinate

The vertical line or $y$-axis in a rectangular Cartesian coordinate system.

Origin

The point where the coordinate axes cross in a Cartesian coordinate system.

Quadrants

The four regions (Quadrant I, Quadrant II, Quadrant III, and Quadrant IV) into which a two-dimensional Cartesian coordinate system is divided.

Relation ($R$)

A set of ordered pairs that connects elements of one set to elements of another set, where every relation is a subset of the Cartesian product ($A \times B$).

Cartesian Product ($A \times B$)

The set of all ordered pairs $(x, y)$ formed such that $x \in A$ and $y \in B$.

Domain of a Relation

The set of all first components in the ordered pairs of a relation, formally expressed as $\{x : (x, y) \in R\text{ for some }y\}$.

Range of a Relation

The set of all second components in the ordered pairs of a relation.