The domain of the relation is the set of the first elements in the ordered pair.
The range of the relation is the set of the second elements in the ordered pair.

REMEMBER:
Relation:
set of ordered pairs
In ordered pairs, the order of the two values or elements is important.
A relation can be described other than as a set of ordered pairs:
  • by a table of values
  • in words
  • by an equation

Identifying the domain and range from a table of values:
The domain will be the values on the left side, while the range will be the values on the right side.
The unit and the values on the left will go on the horizontal line. This means that the values will be the x-coordinates or the domain.
The unit and the values on the right will go on the vertical line. This means that the values will be the y-coordinates or the range.


Example 1


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For this table of values, the domain is {2, 1, 0, -1, -2}, and the range is {3, 4, 5, 6, 7}.


Example 2: Distance from a flash of lightningtov3.jpg
To find the distance between you and a flash of lightning, count the number of seconds that elapse before you hear the thunderclap. With every kilometre, the time that elapses increases by 3 seconds.

If we were graphing this table of values, the time (s) values would be recorded on the x-axis and the distance (km) values would be recorded on the y-axis. They would become x and y values. The x-values/time (s) values would be the domain, and the y-values/distance (km) values would be the range.


Idenifying the domain and range from a graph:
First, identify the ordered pair of the point on the graph.
The first value (x-coordinate) will be the domain and the second value (y-coordinate) will be the range.

For example:
The ordered pair for A is A(2, 3). This means that the domain is 2 and the range is 3.
The ordered pair for B is B(3, 2). This means that the domain is 3 and the range is 2.
The ordered pair for C is C(-2, -3). This means that the domain is -2 and the range is -3.

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Identifying the domain and range from a word description of a relation:
First, try and record the results in a table of values.
Assume that the table of values was going to be graphed:
The values on the left side would be placed on the x-axis and the values on the right side would be placed on the y-axis. They would now become x and y-coordinates.
The domain would be the x-coordinates or the numbers on the left side, and the range would be the y-coordinates or the numbers on the right side.
If it makes it easier for you, after recording the results in a table of values, you can write the numbers as ordered pairs. The first element/number is the domain, and the second element/number is the range.

For Example:
Let x equal the number of hexagons in each diagram and y equal the number of toothpicks in each diagram.

To find the domain and range of this word equation, record the results in a table of values.

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yaaaaaaay2.JPG

yaaaaaaay3.JPG
yaaaaaaay4.JPG
tov4.JPG
The values under the number of hexagons would be on the x-axis if we were graphing this table of values and the number of toothpicks would be on the y-axis. Remember that the domain is the x-values and the range is the y-values. This means that the domain for this table of values would be {1, 2, 3, 4} and the range would be {6, 11, 16, 21}.


A few questions for practice:

1. Decide if each statement is always true, sometimes true, or always true. Explain.
a) A point with one positive coordinate and one negative coordinate lies in the 4th quadrant.
b) A point whose x- and y- coordinates are equal lies in the 1st or 3rd quadrant.
c) The points on a vertical line have the same x- coordinate.

2. Use the table below
a) Identify the domain
b) Identify the range
c) Write the x and y values in ordered pairs
d) Using this relation, what is the range if the domain is 7

x
y
0
4
1
6
2
8
3
10