The function shifts alphabetic characters (lowercase and uppercase) by 6 positions in the alphabet, wraps around if it exceeds 'z' or 'Z', and leaves non-alphabetic characters unchanged.

[CODE]: 
```python
def approximated_function(s):
    output = ''
    for char in s:
        if char.isalpha():
            shift = 6
            if char.islower():
                output += chr(((ord(char) - ord('a') + shift) % 26) + ord('a'))
            else:
                output += chr(((ord(char) - ord('A') + shift) % 26) + ord('A'))
        else:
            output += char
    return output
```