FUNCTIONS
I N T E G R AT E D M AT H E M AT I C S
6.1 DOMAIN AND RANGE
Objectives
Students will be able to:
1. identify the domain and range of a
relation.
2. show relations as sets and mappings.
DEFINITIONS
• A relation is a set of ordered pairs.
{(5,6),(2,7)}
• The domain of a relation is the set of all its xcoordinates.
• The range of a relation is the set of all its ycoordinates.
EX. 1) GIVEN THE RELATION
{(3,2), (1,6), (-2,0)},
FIND THE DOMAIN AND RANGE.
THE RELATION {(2,1), (-1,3), (0,4)}
CAN BE SHOWN BY
1) a table.
2) a mapping.
3) a graph.
EX.2) GIVEN THE FOLLOWING TABLE, SHOW
THE RELATION, DOMAIN, RANGE, MAPPING.
x -1 0 4 7
y 3 6 -1 3
Example 3
X
1
0.8
0.6
0.4
0.2
Y
1.4
1.2
1
0.8
0.6
• Write the relation,
domain, range, and
mapping from the given
table.
TRY THESE
WRITE THE DOMAIN, RANGE, RELATION, GRAPH , ORDERED
PAIRS, AND MAPPING OF THE FOLLOWING TABLE.
X
7
7
7
5
5
Y
5
16
9
6
23
X
Y
13
5
-1
8
19
-6
0
9
5
23
X
-5
6
5
-5
8
Y
3
3
3
6
99
6.2 FUNCTIONS
Objectives
Students will be able to:
1. To determine if a relation is a
function.
2. To find the value of a function.
FUNCTIONS
A function is a relation in which each element of the domain
is paired with exactly one element of the range. Another way
of saying it is that there is one and only one output (y) with
each input (x).
x
f(x)
y
FUNCTION NOTATION
y  f x 
Input
Output
Name of
Function
DETERMINE WHETHER EACH RELATION
IS A FUNCTION.
Ex.1) {(2, 3), (3, 0), (5, 2), (4, 3)}
DETERMINE WHETHER THE
RELATION IS A FUNCTION.
Ex. 2)
{(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
Try These
Determine if the following are functions?
1.{(1,3), (2,3), (3,3)}
2.{(4,6), (8,9), (10,6)}
3.{(-4,3), (0,9), (23,-15)}
4.{(-1,7), (-4,13), (-4,23)}
VERTICAL LINE TEST (PENCIL TEST)
If any vertical line passes through more
than one point of the graph, then that
relation is not a function.
Are these functions?
VERTICAL LINE TEST
IS THIS A GRAPH OF A FUNCTION?
GIVEN F(X) = 3X - 2, FIND:
1) f(3)
2) f(-2)
GIVEN H (Z) =
2
Z
- 4Z + 9, FIND H (-3)
TRY THESE
1.Given g(x) = x2 – 2, find g(4)
2.Given f(x) = 2x + 1, find f(3) – f(1)