To complete the table with values that ensure the relation is a function, we need to identify a consistent pattern between the input and output values. Here, the inputs and outputs are as follows:
| Input | Output |
|-------|--------|
| 0 | 1 |
| 1 | 4 |
| 2 | 9 |
| 5 | 11 |
| 6 | 15 |
| ? | 20 |
Given the values:
- Input 0 gives Output 1
- Input 1 gives Output 4
- Input 2 gives Output 9
- Input 5 gives Output 11
- Input 6 gives Output 15
We need to determine a pattern or rule that explains these pairs and use it to find the missing input value corresponding to the output 20.
Upon analyzing the pattern, it turns out that there is no clear, single consistent mathematical function that fits all the given pairs unequivocally. This difficulty indicates that finding a singular consistent function might require a different approach or review of input-output transformation rules.
Given the conclusion from analyzing the current problem setup, the resulting status confirms:
The relation's pattern is not entirely clear.
Thus, for the missing section to be completed under function rule constraints:
| Input | Output |
|-------|--------|
| ... | ... |
| ? | 20 |
The appropriate formal result is:
```
Pattern not clear
```
