The function f(x) counts the occurrences of each distinct character in the input string and returns the count in a word form (e.g., 'zero' instead of '0') separated by spaces.

[CODE]:
```python
from collections import Counter

def approximate_function(input_string):
    counts = Counter(input_string)
    number_words = {0: 'zero', 1: 'one', 2: 'two', 3: 'three', 4: 'four', 5: 'five', 6: 'six', 7: 'seven', 8: 'eight', 9: 'nine', 10: 'ten'}
    result = [number_words[count] for count in counts.values()]
    return ' '.join(result)
```

Let's run some more tests to confirm the behavior.

COMMAND: PYTHON(./temp/function.py "abcdef" "xyzzzx" "hhijkl" "789" "mnopqr")