- The domain of a relation is the set of all first coordinates (x-values) from the ordered pairs.
- Extract the x-coordinates from the given relation \(\{(0,2), (1,9), (-9,6), (-4,7)\}\), which are \(\{0, 1, -9, -4\}\).
- Order the set numerically to get \(\{-9, -4, 0, 1\}\).
- The correct option is \(\boxed{b}\).
Explanation
- Understanding the Domain of a Relation
The domain of a relation consists of the set of all first coordinates, or \(x\)-values, from the given set of ordered pairs. The relation provided is a set of ordered pairs: \(\{(0,2), (1,9), (-9,6), (-4,7)\}\). To find the domain, we extract the first element from each of these pairs.
- Extracting the x-coordinates
From the given ordered pairs \((0,2)\), \((1,9)\), \((-9,6)\), and \((-4,7)\), the first elements are:
- From \((0, 2)\), the x-value is \(0\).
- From \((1, 9)\), the x-value is \(1\).
- From \((-9, 6)\), the x-value is \(-9\).
- From \((-4, 7)\), the x-value is \(-4\).
Collecting these values, we get the set \(\{0, 1, -9, -4\}\).
- Identifying the Correct Option
To write the set in a standard way, it is helpful to list the elements in ascending order. Arranging the numbers \(-9, -4, 0,\) and \(1\) from smallest to largest gives: \(\{-9, -4, 0, 1\}\). Comparing this result with the provided options:
A\(\{1, 4, 9\}\)
B\(\{-9, -4, 0, 1\}\)
C\(\{-9, -4, 1\}\)
D\(\{0, 1, 4, 9\}\)
The result matches option b.
Examples
In real life, identifying the domain is like listing all the unique items you have available to make a selection from. For example, if a store offers specific menu combinations, like (burger, \$10), (pizza, \$12), and (salad, \$8), the domain would be the set of food items {burger, pizza, salad}. Understanding how to isolate the input values from a set of data helps in organizing information for databases, scheduling, and resource management.