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RELATIONS &
FUNCTIONS
OBJECTIVE:
DEFINE RELATION AND
DETERMINE WHETHER
A RELATION IS A
FUNCTION .
Relation
Any set of ordered
pairs.
{(0,-1), (0,1), (1,1),
(2,3) (3,2)}
Domain
The x value in an
ordered pair.
(0,5) (1,-3) (2,0) (3,1)
D = { 0, 1, 2, 3}
Range
The y value in an
ordered pair.
(-1,4) (1,0) (2,5) (3,7)
R = {4, 0, 5, 7}
Function
Each number of the
domain is assigned
exactly one number
of the range.
Relations and Functions
A function is a special type of relation in which each element of the domain is paired
with ___________
exactly one element in the range.
A mapping shows how each member of the domain is paired with each member in
the range.
Functions
 3,1, 0,2, 2,4
Domain
Range
-3
1
0
2
2
4
one-to-one function
Relations and Functions
A function is a special type of relation in which each element of the domain is paired
with ___________
exactly one element in the range.
A mapping shows how each member of the domain is paired with each member in
the range.
Functions
 1,5, 1,3, 4,5
Range
Domain
-1
5
1
3
4
function,
not one-to-one
Relations and Functions
A function is a special type of relation in which each element of the domain is paired
with ___________
exactly one element in the range.
A mapping shows how each member of the domain is paired with each member in
the range.
Functions
5,6,  3,0, 1,1,  3,6
Range
Domain
5
6
-3
0
1
1
not a function
Example
{(1,-1), (2,3), (3,5), (4,8)}
1
2
3
4
-1
3
5
8
Yes a function
Each domain
has one range.
Example
{(0,-1), (0,1), (1,1), (2,3), (3,2)}
0
1
2
3
-1
1
2
3
Not a function
0 has more
then one range.
Vertical Line Test
The vertical line passes
through only one point
at any time.
Relations and Functions
You can use the vertical line test to determine whether a relation is a function.
Vertical Line Test
If no vertical line intersects a
graph in more than one point,
the graph represents a function.
If some vertical line intercepts a
graph in two or more points, the
graph does not represent a function.
y
y
x
x
Relations and Functions
The table shows the population of Indiana over the last several
decades.
We can graph this data to determine
if it represents a function.
Year
Population
(millions)
1950
3.9
1960
4.7
1970
5.2
1980
5.5
1990
5.5
2000
6.1
Population of Indiana
8
7
Population
(millions)
6
Use the vertical
line test.
5
4
3
Notice that no vertical line can be drawn
that contains more than one of the data
points.
2
1
0
‘50
‘60
‘70
‘80
Year
‘90
‘00
0
7
Therefore, this relation is a function!
Relations and Functions
State the domain and range of the relation shown
in the graph. Is the relation a function?
The relation is:
y
(-4,3)
(2,3)
{ (-4, 3), (-1, 2), (0, -4), (2, 3), (3, -3) }
The domain is:
{ -4, -1, 0, 2, 3 }
The range is:
{ -4, -3, 2, 3 }
The relation is a function
x
(-1,-2)
(0,-4)
(3,-3)