Ask a New Question
Menu

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.

double check

3 answers

To ensure that the table represents a function, each input must map to exactly one output. In the table you've provided:

  • Input: 1, 2, 3, 2, 1
  • Output: 5, 10, 15, 20, 24

We can see that the input "2" corresponds to two different outputs: 10 (the second value) and 20 (the fourth value). This violates the definition of a function, which states that each input can have only one output.

To correct this and make it a function, we need to change one of the outputs so that each input maps to only one output. For example, we can change the output corresponding to the second occurrence of input "2" (which currently outputs "20") to, let's say, "12".

Here is the revised table:

  • Input: 1, 2, 3, 2, 1
  • Output: 5, 10, 15, 12, 24

Explanation of Changes:

  1. Changed the output for the second occurrence of input "2" from 20 to 12.

By doing this, we've ensured that:

  • Input "1" maps to output "5"
  • Input "2" maps to output "10" (first occurrence)
  • Input "3" maps to output "15"
  • Input "2" maps to output "12" (second occurrence, but it now consistently maps to only one output)
  • Input "1" maps to output "24" (first occurrence, but it consistently maps to one output)

Now, each input maps to exactly one output, fulfilling the requirement of a function.

I apologize for any misunderstanding in my previous response. Let’s revisit the problem more carefully.

Original Table:

  • Inputs: 1, 2, 3, 2, 1
  • Outputs: 5, 10, 15, 20, 24

Identifying the Issue:

  • Input "2" appears twice, giving two different outputs (10 and 20).
  • Input "1" also appears twice with different outputs (5 and 24).

Both of these create a situation where an input does not have a unique output, which violates the definition of a function.

Making Changes:

To correct the situation, we need to ensure that each input is paired with exactly one output.

  1. Let's change the output for the second occurrence of input "1" (which currently outputs "24") to match the first occurrence's output "5".

Revised Table:

  • Inputs: 1, 2, 3, 2, 1
  • Outputs: 5, 10, 15, 10, 5

Explanation of Changes:

  1. Changed the output for the second occurrence of input "1" (24) to 5.

    • This ensures that all occurrences of input "1" now point to the same output, "5".

  2. Kept the two outputs for the first and second occurrences of input "2" as 10.

    • This ensures input "2" consistently maps to one output, "10".

Summary:

Now, every input maps to exactly one output:

  • Input "1" → Output "5" (for both occurrences)
  • Input "2" → Output "10" (for both occurrences)
  • Input "3" → Output "15"

With these changes, the table fulfills the requirements of representing a function. Thank you for your patience, and I hope this response clarifies the situation!