The function takes input strings and shifts each alphabetic character by 11 positions forward in the alphabet for lowercase letters and -3 positions backward for uppercase letters. Non-alphabetic characters remain unchanged.

[CODE]:
```python
def f(x):
    result = ""
    for char in x:
        if "a" <= char <= "z":
            result += chr(((ord(char) - ord("a") + 11) % 26) + ord("a"))
        elif "A" <= char <= "Z":
            result += chr(((ord(char) - ord("A") - 3) % 26) + ord("A"))
        else:
            result += char
    return result
```

To confirm the description and code, let's test the function again with some inputs.

COMMAND: PYTHON(./temp/function.py "python" "ChecK" "Upper" "tesT")