Question
9 Are the following ordered pairs a function?
Ask by Gardner Harrington. in the United States
Jan 07,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Yes, the set of ordered pairs
Solution
Yes, the given set of ordered pairs is a function.
Explanation:
A function is a relation where each input (often represented as the first element of an ordered pair) is associated with exactly one output (the second element).
Let’s examine the provided ordered pairs:
- Inputs (First Elements): 9, 4, -1
- Outputs (Second Elements): -5, -5, 7
Key Points:
- Uniqueness of Inputs: Each input value (9, 4, -1) is unique; no input is repeated.
- Output Values: While two different inputs (9 and 4) share the same output (-5), this does not violate the definition of a function. A function allows multiple inputs to map to the same output, but each input must map to only one output.
Since every input in the set maps to exactly one output and there are no duplicate inputs with different outputs, the relation satisfies the definition of a function.
Conclusion:
✓ Yes, the set of ordered pairs
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To determine whether the ordered pairs
Additionally, remember that a function is like a vending machine: you choose a button (input), and it gives you a snack (output). If you can hit the same button several times and still get the same snack, that’s completely okay! The key is to ensure that each button leads to a unique snack, which is satisfied in this case. Keep exploring how inputs and outputs interact!
