- Identify all the \(y\)-values in the relation: \(\{0, 2, 4, 2, 0\}\).
- Extract the unique values from this set: \(\{0, 2, 4\}\).
- State the final range as the set of these unique values.
- Final Answer: \(\boxed{\{0, 2, 4\}}\).
Explanation
- Understanding the Concept of Range
The range of a relation is defined as the set of all unique second coordinates (often denoted as \(y\)-values) from the given set of ordered pairs. We are given the following table of ordered pairs \((x, y)\):
\[ @@TABLE_TOKEN_0@@ \]
The set of all \(y\)-values present in the table is \(\{0, 2, 4, 2, 0\}\).
- Identifying Unique y-values
To determine the range, we list all the observed \(y\)-values and keep only the unique ones. The values are:
- \(0\)
- \(2\)
- \(4\)
- \(2\) (duplicate)
- \(0\) (duplicate)
Removing the duplicates, the distinct values are \(0, 2,\) and \(4\). Therefore, the range is the set \(\{0, 2, 4\}\).
- Conclusion
By comparing our calculated range \(\{0, 2, 4\}\) with the given options, we conclude that the correct range is \(\{0, 2, 4\}\). The final answer is \(\boxed{\{0, 2, 4\}}\).
Examples
In everyday life, the concept of range is like tracking the different types of tickets available for a concert. If you list the price of each ticket type, the set of all unique prices represents the range. For example, if you have tickets for balcony seats at \$20, floor seats at \$50, and VIP seats at \$100, the range of prices is \(\{\$20, \$50, \$100\}\). Understanding this helps in organizing data and identifying the unique outcomes in any given set of information.