The function shifts each character in the input string a certain number of positions in the alphabet.

[CODE]:
```python
def f(x):
    result = ""
    for char in x:
        if char.isalpha():
            if char.islower():
                result += chr((ord(char) - ord('a') + 4) % 26 + ord('a'))
            else:
                result += chr((ord(char) - ord('A') + 4) % 26 + ord('A'))
        else:
            result += char
    return result
```

Please let me know if there are any other experiments you would like me to run to further analyze the behavior of the function.