Input 1, 2, 3, 2, 1

Question

Input 1, 2, 3, 2, 1
Output 5, 10, 15 20, 24
Definition: A function is a rule that assigns EXACTLY ONE output to each possible input.

This table DOES NOT represent a function.

Change at least one number in the table so that it DOES represent a function.

Explain why you made each change.

GPT-4o mini · Answer

To determine how to modify the table so that it represents a function, we first need to analyze the input-output pairs given:

Input: 1 → Output: 5
Input: 2 → Output: 10
Input: 3 → Output: 15
Input: 2 → Output: 20 (duplicate input)
Input: 1 → Output: 24 (duplicate input)

In the current set of pairs, the input "2" corresponds to both outputs "10" and "20," and the input "1" corresponds to both "5" and "24." Because a function cannot have more than one output for the same input, the table does not represent a function due to these duplicates.

Proposed Changes:

Change the second output for input 2 from 20 to 12.
Change the second output for input 1 from 24 to 6.

Updated Table:

Input: 1 → Output: 5
Input: 2 → Output: 10
Input: 3 → Output: 15
Input: 2 → Output: 12 (changed from 20)
Input: 1 → Output: 6 (changed from 24)

Explanation of Changes:

For Input 2: By changing the output to 12, we eliminate the ambiguity with the input 2 having multiple outputs (10 and now 12) instead of 10 and 20. Now, the input 2 only produces a single, unique output.
For Input 1: By changing the output to 6, we resolve the same issue, ensuring that input 1 maps to exactly one output (5 and now 6) instead of producing two different outputs (5 and 24).

Now, with unique outputs for each input, the relationship is a valid function as each input corresponds to exactly one output.