The function shifts each alphabetical character in the input string forward by one (with wrap around) and adds "Z" to the end of the string.

[CODE]:
```python
def f(x):
    shifted_string = ''
    for char in x:
        if 'a' <= char <= 'z':
            shifted_string += chr(((ord(char) - ord('a') + 1) % 26) + ord('a'))
        elif 'A' <= char <= 'Z':
            shifted_string += chr(((ord(char) - ord('A') + 1) % 26) + ord('A'))
        else:
            shifted_string += char

    return shifted_string + 'Z'
```

Please test this code to verify if it behaves similar to the given function.