For a given input string, the function returns the input as a word if it is a single-digit number or 10, 'zero' for the numbers '2' and '22', and an empty string for all other inputs.

[CODE]:
```python
def approximate_function(input_string):
    number_words = {
        '1': 'one',
        '2': 'zero',
        '3': 'three',
        '4': 'four',
        '5': 'five',
        '6': 'six',
        '7': 'seven',
        '8': 'eight',
        '9': 'nine',
        '10': 'one',
    }

    if input_string in number_words:
        return number_words[input_string]
    elif input_string == '22':
        return 'zero'
    else:
        return ''
```
