In Lesson 1-6, you learned that data can be represented in a table. The table at the right shows the estimated number of sea turtles found stranded on the Texas Gulf Coast over several months in a recent year.
The data can also be represented by a set of ordered pairs,
as shown below. Each first coordinate represents the month, and the second
coordinate is the number of stranded sea turtles.
{(1, 22), (2, 29), (3, 43), (4, 76),
(5, 41), (6, 23)}
The first coordinate in an ordered pair is called the x-coordinate. The second coordinate is
called the y-coordinate.
Each ordered pair can be graphed.
A set of ordered pairs, such as the one for the sea turtle
data, is a relation.
The set of all first coordinates of the ordered pairs, or x-coordinates,
is called the domain
of the relation. The set of all second coordinates, or y-coordinates,
is called the range.
For the relation of the sea turtle data, the domain is {1, 2,
3, 4, 5, 6}, and the range is {22, 29, 43, 76, 41, 23}.
A relation can be shown in several ways. Three ways of
representing the relation {(1, 1), (0, 2), (1, 3)} are shown below.
Example
1. Express the relation {(–2, 4), (2, 5), (3, 3), (4, 2), (5, –1)} as a
table and as a graph. Then determine the domain and range.
Alternative Solutions :
The domain
is {–2, 2, 3, 4, 5}, and the range is {4, 5, 3, 2, –1}.
2. Express the relation shown on the graph as a set of ordered pairs and in
a table. Then determine the domain and range.
Alternative Solutions :
The
set of ordered pairs for the relation is {(–3, –1), (–2, 5), (1, 2), (2, –3),
(5, 4)}.
The domain
is {–3, –2, 1, 2, 5}, and the range is {–1, 5, 2, –3, 4}.
In real-life situations, you may need to select a range of
values for the x- or y-axis that does not begin with 0.
Example
Demographics Link
3. The table shows the population of Kentucky since 1930.
A. Determine the domain and range of
the relation.
B. Graph the relation.
C. During which decade was there the
greatest increase in population?
Alternative Solutions :
A. The domain is
{1930, 1940, 1950, 1960, 1970, 1980, 1990, 2000}.
The range is {2.6, 2.8, 2.9, 3.0, 3.2, 3.7,
4.0}.
B. The x-coordinates
go from 1930 to 2000. The scale does not
have to begin at
0. The y-coordinates include values
from 2.6 to 4.0.
You can include 0 and use units of 0.2.
C. The graph shows
that the greatest increase in population
was during the
1970s.
Sumber
Thanks for reading Relations. Please share...!
