The function capitalizes the first character of the input string and duplicates the second character.

[CODE]:
```python
def approximate_function(s):
    if len(s) < 2:
        return s.upper()
    return s[0].upper() + s[1] * 2 + s[2:]
```
Now let's do another test with short strings and empty string to verify the behavior for them as well.

COMMAND: PYTHON(./temp/function.py "" "a" "A" "zZ")