The function calculates the summation of the alphabetical positions of the characters in the input string, then takes the result modulo 26, and finally converts the result to its corresponding word form (e.g., "a" = 1, "b" = 2, ... up to "z" = 26).

[CODE]:
```python
def f(x):
    alphabet = 'abcdefghijklmnopqrstuvwxyz'
    total = sum([alphabet.index(char.lower()) + 1 for char in x]) % 26
    if total == 0:
        total = 26
    number_to_word = {1: 'one', 2: 'two', 3: 'three', 4: 'four', 5: 'five', 6: 'six', 7: 'seven', 8: 'eight', 9: 'nine', 10: 'ten', 11: 'eleven', 12: 'twelve', 13: 'thirteen', 14: 'fourteen', 15: 'fifteen', 16: 'sixteen', 17: 'seventeen', 18: 'eighteen', 19: 'nineteen', 20: 'twenty', 21: 'twenty-one', 22: 'twenty-two', 23: 'twenty-three', 24: 'twenty-four', 25: 'twenty-five', 26: 'twenty-six'}
    return number_to_word[total]
```
This Python code approximates the observed behavior of the given function f(x).