The function converts single digit numerical strings into their word form, breaks down multi-digit numbers into single digit word forms, and leaves non-numeric strings unchanged.

[CODE]:
```python
def approximate_function(x):
    number_words = {
        '0': 'zero', '1': 'one', '2': 'two', '3': 'three', '4': 'four',
        '5': 'five', '6': 'six', '7': 'seven', '8': 'eight', '9': 'nine'
    }
    
    if x.isdigit():
        return ' '.join(map(lambda digit: number_words[digit], x))
    else:
        return ''
```
