- The range of a relation is the set of all y-coordinates in the given ordered pairs.
- Extract the second values: \(-3, -8, 6, 2\).
- Organize these values into a set and order them numerically: \(\{-8, -3, 2, 6\}\).
- The final answer corresponds to option (b), which is \(\boxed{\{-8, -3, 2, 6\}}\).
Explanation
- Identifying the Second Coordinates of the Relation
The range of a relation is defined as the set of all possible output values, which are represented by the second coordinate (the y-coordinate) in each ordered pair of the relation. We are given the relation defined by the set of ordered pairs:
\[ S = \{(-8, -3), (-3, -8), (-1, 6), (4, 2)\} \]
To find the range, we identify the second coordinate of each pair in the set. The set of all second coordinates is \(\{-3, -8, 6, 2\}\).
- Formatting and Identifying the Correct Option
Once we have extracted the second coordinates, we express them as a set:
\[ \{-3, -8, 6, 2\} \]
It is standard practice to list the elements of a set in increasing order. Sorting these values from least to greatest, we get:
\[ \{-8, -3, 2, 6\} \]
Comparing this to the provided options, we see that it corresponds to option (b).
Examples
In real life, the concept of a domain and range can be seen when looking at a parking meter system where each car license plate (domain) is mapped to a unique parking spot number (range). If you have a log of transactions, you can easily identify all the spots that were occupied by checking the list of secondary entries in your records. This helps in inventory management and ensuring efficient space utilization.