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General Mathematics: RELATIONS AND FUNCTIONS

Grade 11

A RELATION is a set of ordered pairs. The DOMAIN of a relation is the set of first coordinates. The RANGE is the set of second coordinates.

Ex.
A= { (1,2) , (3,4) ,( 5,6) , (7,8) }
Domain; {(1,3,5,7)}
Range; { (2,4,6,8) }

The special kind of relation is called function. A FUNCTION is a relation in which each element of the domain corresponds to exactly one element of the range.

Ex.
{ (I,4), (L,5) , (O,6) ,( V, 8 ) , (E,3) ,(M,6) ,(A,2) ,(T,8), (H,4) }

Domain; { I,L,O,V,E,M,A,T,H}
Range; {2,3,4,5,6,8}

This relation is function,since each element in the domain is assigned one element in the range. Even though the range element 4 is assigned two elements of the domain, I ,and H, it is still function since each element of the domain is assigned to only one element of the range.

Function can be "One to one" or "Many to one"

Ex. ONE to ONE
{ (1,6),(2,5) , (3,7) }
Domain : { 1,2,3 }
Range : { 6,5,7}

Ex. MANY TO ONE
{ (2,7) ,(4,7),(6,7) (8,9) }
Domain: { 2,4,6,8}
Range: { 7,9 }

4 Ways of Expression a Relation

1.) Mapping Diagram
2.) Table of Values
3.) Graph
4.) Equation

The Vertical Line Test -a graph represent a function if and only if no vertical line intersects the graph in more than one point.

Source: RBS Mathematics Series,E-Math IV, (Orlando A. Oronce and Marilyn O.Mendoza, 2010)

— Awansik, Balnian, Haykapnayan, Lakta

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