These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide:
Relations

A relation is a set of ordered pairs. The domain of a relation is the set of all first coordinates of the ordered pairs, and the range is the set of second coordinates.

Relations may be expressed in the form of ordered pairs, tables, graphs, and mappings.

The inverse of any relation is obtained by switching the coordinates in each ordered pair.

 

Refined terminology of a relation.

Later, in your study of mathematics, the term "relation" takes on a slightly different meaning once functions have been introduced. A function is defined as a relation that assigns each value of x to exactly one unique value of y.

Consequently the term relation is used to refer to a collection of points in which a value of x can be associated/paired to more than one value of y.

For example,

  • the graphs of x = 2 and x = y2 are just called relations; while
  • the graphs of y = 2 and y = x2 are functions usually written with the notation f(x) instead of just y

 

Directions: State the domain and range of each relation.

Directions: Express the relations shown in each table, mapping, or graph as a set of ordered pairs. Then state the domain, range, and inverse of the relation.

Directions: Draw a mapping and graph for each relation.