RELATION
DEFINITION:
ANY SET OF ORDERED PAIRS.
ANY TIME YOU SEE THE WORD SET IT
MEANS THAT IT SHOULD BE PLACED IN
{ }, BRACES.
EXAMPLE:
{(3, 2), (-4, 7), (6,-3)}
RELATION
RELATIONS CAN BE SHOWN SEVERAL
DIFFERENT WAYS:
1.
2.
3.
4.
SET OF ORDERED PAIRS
TABLE
MAPPING
GRAPH
RELATION EXAMPLES
1. SET OF ORDERED PAIRS:
{(3, 2), (-4, 7), (6,-3)}
{(5,2), (-1,2), (3,3), (-6,2)}
WHEN A RELATION IS SHOWN THIS
WAY IT MUST BE PUT INSIDE
BRACES. { }
2. RELATION SHOWN AS A
TABLE
{(3,2), (-4,7),(6,-3),(4,5)}
X
3
Y
2
-4
7
6
-3
4
5
3. RELATION SHOWN AS A
MAPPING
RELATION SHOWN IS { (-2,4), ( 2,4), (4,16), (5,25), (6,36)}
If any x or y values are the same you do not list them more
once in the circle.
4. RELATION SHOWN AS A
GRAPH
{(5,2), (-1,2), (3,3), (-6,2)}
EXAMPLE
• EXPRESS THE RELATION AS A TABLE, A
MAPPING AND A GRAPH.
{(0,0), (-1,2), (3,3), (-4,-4), (5,-3), (0,3)}
x
y
x
y
EXAMPLE
WRITE THE FOLLOWING TABLE AS A
RELATION.
X
Y
4
0
5
-1
-2
6
3
2
EXAMPLE
WRITE THE FOLLOWING MAPPING AS A
RELATION.
1
2
3
0
-1
6
2
EXAMPLE
WRITE THE FOLLOWING GRAPH AS A
RELATION.
DOMAIN OF A RELATION
• DEFINITION:
IS THE SET OF X VALUES IN A RELATION.
MUST BE WRITTEN INSIDE BRACES { }
• EXAMPLE:
{(5,2), (-1,2), (3,3), (-6,2)}
DOMAIN = { 5, -1, 3, -6 }
DO NOT REPEAT THE SAME NUMBER IN THE
DOMAIN OF A RELATION.
RANGE OF A RELATION
• DEFINITION:
THE SET OF DIFFERENT Y-VALUES IN A RELATION.
THIS MEANS IT MUST BE WRITTEN INSIDE BRACES
{ }.
• EXAMPLE:
{(5,2), (-1,2), (3,3), (-6,2)}
RANGE = { 2, 3 }
DO NOT REPEAT THE SAME NUMBER WHEN STATING
THE RANGE OF A RELATION.
EXAMPLES OF DOMAIN AND
RANGE OF A RELATION
• RELATION:
{(9, 4), (-3, 8), (2, 0), (-3, 7)}
• DOMAIN = {
}
• RANGE = {
}
INVERSE RELATION
• DEFINITION:
IS THE RELATION FORMED WHEN THE
X AND Y VALUES OF EACH ORDERED
PAIR ARE SWITCHED.
EXAMPLE:
(3,4) BECOMES (4,3) IN AN INVERSE
RELATION
EXAMPLE OF AN INVERSE
RELATION
• RELATION:
{(9, 4), (-3, 8), (2, 0), (-3, 7)}
• INVERSE RELATION:
{(4, 9), (8,-3), (0, 2), (7,-3)}