- A function requires each input \(x\) to map to exactly one output \(y\).
- Examining Table 1: Inputs \(\{-3, 0, -2, 8\}\) are all unique, so it is a function.
- Examining Table 2, 3, and 4: Each of these tables contains at least one input that maps to two different output values.
- Therefore, only Table 1 represents a function.
- Final answer: \(\boxed{\text{Table 1}}\)
Explanation
- Definition and Strategy for Identifying a Function
A function is defined as a relation where every input value \(x\) is associated with exactly one output value \(y\). To determine which of the provided tables represents a function, we must check each table to see if any input value \(x\) maps to more than one output value \(y\). If we find an \(x\) value that appears more than once with different \(y\) values, that table fails the definition of a function.
- Evaluating the Provided Tables
We examine the four tables:
- Table 1: The input values are \(\{-3, 0, -2, 8\}\). Each input value appears exactly once. Since every input is unique, there is no chance of an input mapping to multiple outputs. Thus, this table represents a function.
- Table 2: The input values are \(\{-5, 0, -5, 6\}\). The input value \(-5\) appears twice: once with an output of \(-5\) and once with an output of \(5\). Since \(-5\) maps to two different values, this table is not a function.
- Table 3: The input values are \(\{-4, -2, -2, 0\}\). The input value \(-2\) appears twice: once with an output of \(2\) and once with an output of \(4\). Since \(-2\) maps to two different values, this table is not a function.
- Table 4: The input values are \(\{-4, 3, 1, -4\}\). The input value \(-4\) appears twice: once with an output of \(2\) and once with an output of \(0\). Since \(-4\) maps to two different values, this table is not a function.
- Conclusion
After evaluating each table, we conclude that only the first table satisfies the condition where every input \(x\) maps to exactly one output \(y\). Therefore, the first table is the only one that represents a function.
\(\boxed{\text{Table 1}}\)
Examples
In daily life, the concept of a function is used to ensure consistency in data mapping. For instance, if you have a vending machine, each button code (the input \(x\)) should always dispense the same specific snack (the output \(y\)). If pressing button 'A1' could randomly result in either a bag of chips or a chocolate bar, the vending machine's mapping would not be a function. This property of consistency is essential in computer programming, database management, and even simple organizational tasks.