The function f(x) takes a string input and shifts each alphabetical character forward by a fixed number of positions in the alphabet while preserving non-alphabetical characters (e.g. digits, spaces) unchanged. The resultant string is returned as the output.

[CODE]:
```python
def shift_alphabets(s, shift=3):
    result = []
    for char in s:
        if char.isalpha():
            if char.isupper():
                result.append(chr(((ord(char) - 65 + shift) % 26) + 65))
            elif char.islower():
                result.append(chr(((ord(char) - 97 + shift) % 26) + 97))
        else:
            result.append(char)
    return "".join(result)
```
Let's confirm the description with some more test cases.

COMMAND: PYTHON(./temp/function.py "xyZ9" "Shift3" "aBc_dEf!" "end")