The function seems to be swapping the first two characters in the input string. If the first character is non-alphabetic (non-letter), it remains in the same position, and the second character is swapped with the first alphabetic character found in the string.

[CODE]: 
```python
def approx_function(s):
    if not s:
        return s
    if not s[0].isalpha():
        for i in range(1, len(s)):
            if s[i].isalpha():
                s = s[0:i] + s[i] + s[1:i] + s[i+1:]
                break
    else:
        s = s[1] + s[0] + s[2:]
    return s
```