Based on the output of the function for the inputs 'world', 'zoo', and '123', we can observe that:
- The function is shifting each character by a fixed number of positions in the alphabet.
- Non-alphabet characters, such as digits or special characters, are not shifted.

Based on these observations, we can approximate the behavior of the function with the following description:

[DESCRIPTION]:
The function takes an input string and shifts each alphabetical character by a fixed number of positions in the alphabet. Non-alphabet characters remain unchanged.

[CODE]:
```python
def f(x):
    result = ""
    for char in x:
        if char.isalpha():
            shifted_char = chr((ord(char) - 97 + shift) % 26 + 97)
            result += shifted_char
        else:
            result += char
    return result

shift = <fixed number specifying the shift>
input_string = "<input string>"
output_string = f(input_string)
print(output_string)
```

Please note that in the code, the `<shift>` variable needs to be replaced with the actual number specifying the shift, and the `<input string>` variable needs to be replaced with the actual input string.