Question

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.

input
1
2
3
2
1

output
5
10
15
20
24

Answer 1

so what change do I make?

Answer 2

explain why I changed it

Answer 3

To ensure that the table represents a function, each input must be associated with exactly one output. In the current table, the input "2" is associated with both "10" and "20," which means it does not fit the definition of a function.

To fix this, we can change one of the outputs associated with the input "2." For example, we can change the output that corresponds to the second occurrence of the input "2" (20) to a different value, such as 12.

Here’s the modified table:

```
input
1
2
3
2
1

output
5
10
15
12
24
```

Now, the input "2" is associated with only one output (10 and 12), making it a function.

Answer 4

You need to change the output for the second occurrence of the input "2."

Currently, the table looks like this:

```
input
1
2
3
2
1

output
5
10
15
20
24
```

Change the output for the second "2" (currently 20) to a different value. For example, you could change it to 12.

Here’s the revised table:

```
input
1
2
3
2
1

output
5
10
15
12
24
```

Now, each input has a unique associated output, and it satisfies the definition of a function.

Answer 5

You changed the output for the second occurrence of the input "2" because a function, by definition, must assign exactly one output to each possible input. In the original table, the input "2" was associated with two different outputs:

- The first instance of input "2" had an output of **10**.
- The second instance of input "2" had an output of **20**.

This violates the rule of functions because it means that the input "2" does not correspond to a unique output—there are multiple outputs for the same input.

To make the table represent a function, it's necessary to ensure that each input corresponds to one and only one output. By changing the output for the second occurrence of "2" (from **20** to **12**), you created a scenario where both occurrences of "2" now correspond to one unique output each (10 for the first occurrence and 12 for the second).

This action resolves the duplication issue and meets the definition of a function, where each input has a distinct and single output.