The function increments each alphabet character in the input string by 3 positions in the alphabet and keeps numbers and special characters unchanged.

[CODE]: 
```python
def f_approx(x):
    result = ""
    for char in x:
        if char.isalpha():
            if char.islower():
                result += chr(((ord(char) - ord('a') + 3) % 26) + ord('a'))
            else:
                result += chr(((ord(char) - ord('A') + 3) % 26) + ord('A'))
        else:
            result += char
    return result
```

Let's run one final test for confirmation. 

COMMAND: PYTHON(./temp/function.py "Advanced" "Example123!")