- Identify the first coordinate (x-value) from each ordered pair in the set: \(-4, 8, 9, 1, 1\).
- Extract the unique values from this list to form the domain set: \(-4, 1, 8, 9\).
- The domain is the set of these unique values ordered as \(\{-4, 1, 8, 9\}\).
- The final answer is \(\boxed{\{-4, 1, 8, 9\}}\).
Explanation
- Understanding the Domain of a Relation
The domain of a relation is defined as the set of all first coordinates (also known as the x-values) of the ordered pairs that form the relation. Given the relation defined by the set of ordered pairs \(\{(-4, 4), (8, -1), (9, -9), (1, 2), (1, 8)\}\), we need to extract these first coordinates to determine the domain.
- Identifying Unique x-coordinates
The first coordinates (x-values) of the ordered pairs in the given relation are \(-4, 8, 9, 1,\) and \(1\). To find the domain, we compile these values into a set. A set by definition only contains unique elements, so we list each distinct value exactly once. The unique values in our list are \(-4, 8, 9,\) and \(1\). Rearranging these in ascending order, we obtain the set \(\{-4, 1, 8, 9\}\).
- Conclusion and Selection
Comparing our derived set \(\{-4, 1, 8, 9\}\) with the provided options, we see that it matches the first option. Therefore, the domain of the given relation is \(\{-4, 1, 8, 9\}\).
Examples
In real-life scenarios, the concept of a domain is used in data management and database design. For example, if you have a list of students (first value) and their corresponding test scores (second value), the "domain" would be the list of all unique students who took the test. Identifying this set helps ensure that you have a complete and non-redundant list of participants for data analysis or grading purposes. Understanding how to extract unique elements is a fundamental skill for organizing information accurately.