Download Notes/Math/9R Relations

Do Now
Use the graph paper and the ruler to make a set of
axes and graph the points:
A (1,4)
B ( – 2,3)
C (4, – 5)
D (– 5, – 3)
E (3,1)
Do you remember how to label the quadrants?
Graphing & Quadrants Review
y
Quadrant II
Quadrant I
X is –
X is + and Y is +
and Y is +
x
Quadrant III
Quadrant IV
X is – and Y is –
X is + and Y is –
Notes On Graphing
Points are located on the coordinate plane.
Points are also called ordered pairs.
(x, y)
The x-coordinate tells you how many units to
move right/left.
The y-coordinate tells you how many units to
move up/down.
RELATIONS
A relation is a set of ordered pairs.
Ways to represent a relation:
ORDERED PAIRS
•(3,4)
•(-2,8)
•(-4,-9)
TABLE
X
3
-2
-4
Y
4
8
-9
MAPPING
X
Y
3
-2
-4
4
8
-9
OR YOU CAN GRAPH THE POINTS
Example – Ken Griffey, Jr.’s home run and
strikeout numbers can be summarized as
follows for the years 1994 – 2001.
(HR, S.O.) (40, 73), (17, 53), (49, 104), (56, 121),
(56, 121), (48, 108), (40, 117), (22, 72).
Show this relation as a table, graph and mapping.
Home Runs StrikeOuts
40
73
17
53
49
104
56
121
56
121
48
108
40
117
22
72
(HR, S.O.) (40, 73), (17, 53), (49, 104), (56, 121),
(56, 121), (48, 108), (40, 117), (22, 72).
140
Graph:
120
100
80
60
40
20
-100
-50
50
-20
100
(HR, S.O.) (40, 73), (17, 53), (49, 104), (56, 121),
(56, 121), (48, 108), (40, 117), (22, 72).
Mapping:
40
73
17
53
49
104
56
121
56
121
48
108
40
117
22
72
Domain & Range
The domain of a relation is the set of all x –
values.
The range of a relation is the set of all yvalues.
(Remember they’re in alphabetical order)
a. Express the relation {(3, –2), (4, 6), (5, 2), (–1, 3)}
as a table, a graph, and a mapping.
Answer:
x
y
3
4
5
–2
6
2
–1
3
b. Determine the domain and range.
Answer: D = {–1, 3, 4, 5}; R = {–2, 2, 3, 6}
JUST SWITCH THE COORDINATES IN EACH PAIR
EXAMPLES: Find the inverse of each relation. Then state the
domain and range of each inverse.
1) (-9,5) (3,-7)
2)
X
-9
4
Y
7
8
(-5,-6)
(3,7)
3.
-3
-5
8
4
7
4
-3
5
Express the relation shown in the mapping as a set of
ordered pairs. Then write the inverse of the relation.
Answer: Relation: {(3, 2), (–4, 1), (5, 2)}
Inverse: {(2, 3), (1, –4), (2, 5)}