Question

#7.
Input
Output
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.

Answer 1

To make the table represent a function, we need to ensure that each input corresponds to exactly one output. Here’s an example of how to make changes to a hypothetical table.

### Original Table:
| Input | Output |
|-------|--------|
| 1 | 2 |
| 2 | 3 |
| 2 | 4 |
| 3 | 5 |

### Changes Made:
- Change the second occurrence of "2" in the input column to "4".

### Updated Table:
| Input | Output |
|-------|--------|
| 1 | 2 |
| 2 | 3 |
| 4 | 4 |
| 3 | 5 |

### Explanation:
1. The original table lists the input "2" twice, which associates it with two different outputs (3 and 4). This means that for the input "2," there is not a single output but rather two possible outputs. This violates the definition of a function.

2. By changing the second input "2" to "4," we ensure that each unique input corresponds to exactly one output. Now, all inputs (1, 2, 4, and 3) have a unique output (2, 3, 4, and 5 respectively).

This change ensures the one-to-one relationship required for a function to be valid.