The function scans the input string and returns a number word ("zero," "one," "two," etc.) based on the position of the first occurrence of "1", "2", or "3". If none of these characters are in the input string, the output will be an empty string. 

[CODE]:
```python
def approximate_function(s):
    for idx, char in enumerate(s):
        if char in ['1', '2', '3']:
            number_words = ["zero", "one", "two", "three", "four", "five", "six", "seven", "eight", "nine", "ten"]
            return number_words[idx]
    return ""
```
Please note that this is an approximation based on the tests we conducted. The actual function might still have some differences or additional behavior.