GENERAL MATHEMATICS
Topic: Relations and Functions
RELATIONS
TYPES OF RELATIONS
A relation is a rule that relates values from a set of
values (called the domain) to a second set of values
(called the range).
A relation is also a set of ordered pairs (x, y).
(x,y)
One to one
X
a
b
c
y
1
2
3
Domain (x)
Many to one
first coordinate in relation; input; independent
X
Range (y)
second coordinate in relation; output; dependent
One to many
X
a
b
c
Many to many
y
1
2
3
a
b
c
y
1
2
3
X
y
1
2
3
a
b
c
FUNCTIONS
is a relation where each element in the domain is
related to exact one element in the range by some rule.
Examples:
Ways of Representing a Function
Mapping Diagram
FUNCTION <:
X
Enrique
Y
Liza
Daniel
Mateo
Vice
Kath
Sarah
Ion
X
a
b
c
Table of Values
y
1
2
3
x
y
a
1
b
2
c
3
d
4
Graph
NOT a Function >:
X
Gerald
Y
Bea
Pia
Kim
Maja
Sarah
Julia
The Vertical Line Test
A graph represents a
function if and only if
each
vertical
line
intersects the graph at
most once.
Note* “The domain of a relation as the set of all possible values that the variable x can take.
A function is a set of ordered pairs (x,y) such that no two ordered pairs have the same x-value but different yvalues. Using functional notation, we can write f(x) = y, read as “f of x is equal to y.”