- The given relation is defined by the set of ordered pairs \(S = \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\).
- By extracting the pairs from each of the three tables, we identify that only the second table contains these specific pairs: \((-6, 4), (-4, 0), (-3, 2),\) and \((-1, 2)\).
- Therefore, the second table correctly represents the given relation.
- Final answer: The second table.
Explanation
- Analyzing the Problem
The goal is to determine which of the provided tables represents the same relation as the set \(S = \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\). A relation is simply a set of ordered pairs \((x, y)\). The order in which these pairs are presented does not change the relation itself. To solve this, we must compare the ordered pairs listed in the given set \(S\) with the pairs listed as rows in each of the three provided tables.
- Identifying the Correct Table
Let's examine the ordered pairs in the set \(S = \{(-6, 4), (-4, 0), (-3, 2), (-1, 2)\}\). These pairs define our target relation. Now, let's extract the ordered pairs from each table:
- Table 1: The pairs are \((-6, -3), (4, 2), (-4, -1), (0, 2)\).
- Table 2: The pairs are \((-6, 4), (-4, 0), (-3, 2), (-1, 2)\).
- Table 3: The pairs are \((6, 4), (4, 0), (3, 2), (1, 2)\).
By comparing these with our target set \(S\), we see that Table 2 contains exactly the same set of ordered pairs: \((-6, 4), (-4, 0), (-3, 2),\) and \((-1, 2)\). The other tables contain different pairs and therefore represent different relations.
- Conclusion
The second table is the only one that matches the given set \(\{(-6,4), (-4,0), (-3,2), (-1,2)\}\). Thus, the correct table is the second one. The final answer is the second option.
Examples
In real life, relations are frequently used to map inputs to outputs, such as when you look up the price of different items in a catalog. For example, if you have a set of products (the x-values) and their corresponding prices (the y-values), this is a relation. Identifying the correct set of pairs is crucial when organizing data in databases or spreadsheets, as it ensures that you correctly associate the correct value (like a price) with its corresponding item (like a product code). Accurate mapping is essential for everything from shopping carts to logistics tracking systems.