Let's Break it Down
Any connection between sets of values is called a relation.
The table shows the connection between the amount of time each student studied for the quiz and the score they earned.
| Student | Amount of Time Studied (minutes) | Quiz Score Earned (percentage) |
|---|---|---|
| 1 | 30 | 84 |
| 2 | 10 | 52 |
| 3 | 15 | 66 |
| 4 | 20 | 84 |
| 5 | 20 | 61 |
| 6 | 60 | 100 |
| 7 | 25 | 94 |
| 8 | 15 | 80 |
| 9 | 0 | 72 |
| 10 | 35 | 90 |
Other than a table, you can also use ordered pairs, graphs, and mapping diagrams to represent the connections among variables. Use the activity below to learn how to create ordered pairs, graphs, and mappings to show relations.
Ordered Pairs
Recall that an ordered pair is a pair of objects. Generally, ordered pairs have the format (x, y).
Express the data from Ms. Kendall’s table using the format (amount of time studied, quiz score earned). Use the table to create the ordered pairs.
The ordered pairs are
(30, 84); (10, 52); (15, 66); (20, 84);
(20, 61); (60, 100); (25, 97); (15, 80); (0, 72);
(35, 90).
Graph
You can display a relation using a coordinate-pair graph.
Display the data from Ms. Kendall’s table on a coordinate-pair graph. Graph “amount of time studied” along the horizontal axis, and graph “quiz score earned” along the vertical axis.
The ordered pairs are (30, 84); (10, 52); (15, 66); (20, 84); (20, 61); (60, 100); (25, 97); (15, 80); (0, 72); (35, 90). Plot the ordered pairs.
Mapping Diagram
A mapping diagram is another way to show how the values in each set are related to each other. The members of each set are shown in a closed oval. The arrows indicate which numbers are related to each other. Notice that each value is listed only once, even if it is repeated in the set. You will learn more about the value of creating mapping diagrams later in this lesson.
Question
Use the ordered pairs (0, 0); (1, 1.69); (2, 3.38); and (3, 5.07) to create a table, where the value of the first number in each pair is the number of pounds of fruit purchased and the second number is the total cost of the fruit in dollars.
| Number of Pounds of Fruit | Total Cost of Fruit (dollars) |
|---|---|
| 0 | 0 |
| 1 | 1.69 |
| 2 | 3.38 |
| 3 | 5.07 |
