- Extract each row of the table as an ordered pair \((x, f(x))\).
- List the pairs: \((0, 5)\), \((4, 2)\), \((6, 9)\), and \((9, 10)\).
- Assemble these pairs into a set notation: \(\{(0, 5), (4, 2), (6, 9), (9, 10)\}\).
- Compare with the given options to confirm the final answer: \(\boxed{\{(0,5), (4,2), (6,9), (9,10)\}}\).
Explanation
- Analyzing the Data from the Table
A relation defined by a table lists inputs (the independent variable \(x\)) and their corresponding outputs (the dependent variable \(f(x)\)). Each row of the table represents an ordered pair \((x, f(x))\), where the first element is the input and the second element is the output. From the given table, we identify the following rows:
- Row 1: \(x = 0\), \(f(x) = 5\), which gives the ordered pair \((0, 5)\).
- Row 2: \(x = 4\), \(f(x) = 2\), which gives the ordered pair \((4, 2)\).
- Row 3: \(x = 6\), \(f(x) = 9\), which gives the ordered pair \((6, 9)\).
- Row 4: \(x = 9\), \(f(x) = 10\), which gives the ordered pair \((9, 10)\).
- Forming the Set of Ordered Pairs and Selecting the Option
A set of ordered pairs representing this relation is the collection of all these pairs. By combining the pairs identified in the first step, we form the set:
\[\{(0, 5), (4, 2), (6, 9), (9, 10)\}.\]
This set directly maps each input value from the first column to its corresponding output value in the second column of the table. Comparing this set to the provided options, it matches the first option perfectly.
- Conclusion
The set \(\{(0, 5), (4, 2), (6, 9), (9, 10)\}\) correctly represents the relation shown in the table, as each pair consists of a value from the \(x\) column matched with its corresponding value in the \(f(x)\) column. Thus, the final answer is the first option, \(\boxed{\{(0,5), (4,2), (6,9), (9,10)\}}\).
Examples
In everyday life, we often encounter tables of values that represent relationships. For example, a bus schedule relates the time of day (input \(x\)) to the bus stop number or location (output \(f(x)\)). By writing this as a set of ordered pairs, we can clearly see the schedule as a mathematical relation, making it easier to analyze departure times and coordinate our travel plans. Understanding how to represent data as ordered pairs is the foundation for creating graphs, which help us visualize trends or patterns in information.