The function checks if the input string contains the letter 'n'. If the input string contains 'n', it returns 'one', otherwise it returns 'zero'.

[CODE]:
```python
def approximate_function(input_string):
    if 'n' in input_string:
        return 'one'
    else:
        return 'zero'
```
Remember that this is an approximation of the behavior we observed and there might be more to the function that we haven't discovered yet.