10.1 Relations
A relation is a set of one or more ordered pairs. It can be described in:
- A set of ordered pairs
- A table
- A graph
- A mapping
- An open sentence in two variables
The domain of a relation is the set of all its first elements or x-coordinates.
The range of a relation is the set of all its second elements or y-coordinates.
The domain and range values should be listed from least to greatest in set
notation and no numbers should be repeated.
Ordered Pairs
(-2, 4)
(0, -3)
(1, 2)
Open Sentence
𝑦 = 2𝑥 − 1
Table
x
-2
0
1
Graph
Mapping
X
y
y
4
-3
2
-2
0
1
4
-3
2
Example 1:
State the relation specified in the table below as a set of ordered pairs. State the
domain and range of this relation.
Ordered Pairs:
Domain:
Range:
x
y
-1
0
1
0
1.5
3
Example 2:
State the relation specified in the mapping below as a set of ordered pairs. State
the domain and the range of the relation.
Ordered Pairs:
x
y
Domain:
1
Range:
0
2
1
3
-2
0
Example 3:
The graph shows the closing price of MAX stock over a period of one week. State
the relation as a set of ordered pairs. State the domain and the range of the
relation.
Ordered Pairs:
Domain:
Range:
Example 4:
Given the domain {−2, 0, 1} of the relation 2𝑥 + 𝑦 = −1 determine the range.
Graph your results.
1. Rewrite the equation in slope-intercept form by solving for y.
2. Make a table with the domain values and then solve for the range.
3. Graph your results.