1
Section 2.6  Functions and Domains
Definition:
A
relation
in mathematics is a set of one or more ordered pairs.
It can be described by:
1. A set of ordered pairs: {(3, 1), (2, 1), (1, 1), (1, 3), (3, 1), (3, 2), (0, 3)}
2. Graphs:
3. Tables:
4. Mappings:
x
y
3
1
2
1
1
1
1
3
3
1
3
2
0
3
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The
DOMAIN
of a relation is the set of all the first elements (the
x
values or
x
coordinates) in the
ordered pairs.
The
RANGE
of a relation is the set of all the second elements (the
y
values or
y
coordinates) in the
ordered pairs.
A
FUNCTION
is a special relation in which each element,
x
, of the domain is paired with
exactly
(only) one
element, called
f
(
x
), of the range.
One way to test a relation to see if it is a function is by
using the vertical line test.
1. Is the given relation a function?
a)
{ }
)
4
,
3
(
),
5
,
2
(
),
1
,
1
(

Domain:
Range:
b)
{ }
)
2
,
3
(
),
5
,
4
(
),
2
,
1
(
Domain:
Range:
c)
{ }
)
2
,
4
(
),
5
,
4
(
),
2
,
1
(
d)
{ }
)
4
,
4
(
),
0
,
0
(
),
1
,
1
(
In the equation
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 Spring '08
 Staff
 Math

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