GNED 03 - Mathematics in the Modern World: Relation and Function

Vocabulary flashcards covering the concepts, definitions, properties, types, and representations of relations and functions from GNED 03.

Relation

A rule that relates values from a set of values (domain) to a second set (range), or any set of ordered-pair numbers.

Domain

The set of all first components or input values ($x$) in a relation or set of ordered pairs.

Range

The set of all second components or output values ($y$) in a relation or set of ordered pairs.

Function

A relation where each element in the domain is related to only one value in the range by some rule, meaning no two ordered pairs have the same $x$-value but different $y$-values.

One-to-One Relation

A type of function where every element in the domain maps to a distinct, unique element in the range.

Many-to-One Relation

A type of function where two or more distinct elements in the domain map to the same single element in the range.

One-to-Many Relation

A type of relation that is not a function because a single element in the domain maps to more than one value in the range.

Many-to-Many Relation

A type of relation that is not a function where multiple elements in the domain map to multiple elements in the range.

Classifications of Relations as Functions

Diagram illustrating that One-to-One and Many-to-One mapping types are functions, whereas One-to-Many and Many-to-Many mapping types are not functions.

Mapping Representation of Functions

A visual representation using set ovals and directed arrows showing how elements in Set A correspond to elements in Set B.

Ways to Represent a Function

The five methods used to represent functional relationships: mapping, ordered pairs, graph, equations, and table of values.

Vertical Line Test

A graphical test to determine if a relation is a function; if a vertical line hits a graph more than once (such as hitting a circle twice), the graph is not a function.

Graph of a Circle ($x^2 + y^2 = 9$)

A circular graph centered at the origin that fails the vertical line test because a vertical line can intersect it twice, demonstrating it is not a function.

Table of Values

A organized arrangement showing input values ($x$), substituted solutions, and output values ($y$) to evaluate whether any $x$-value repeats with a different $y$-value.