The function checks the input string and assigns a numerical value to it based on certain patterns. If the string consists of only alphabetic characters, it assigns the value "one". If the string consists of only numeric characters, it assigns the value "zero". If the string contains a mixture of alphabetic and non-alphabetic characters, it assigns the value "three".

[CODE]:
```python
def f(x):
    if x.isalpha():
        return "one"
    elif x.isnumeric():
        return "zero"
    else:
        return "three"
```
Note: This is an approximation and may not exactly reflect the implementation of the function in `function.py`.