The function shifts each alphabetic character in the input string by 9 positions in the alphabet, regardless of the case, while leaving numeric and special characters unchanged.
[CODE]:
```python
def approximate_function(input_string):
    result = []
    for char in input_string:
        if char.isalpha():
            offset = 9
            new_char = chr(((ord(char.lower()) - ord('a') + offset) % 26) + ord('a'))
        else:
            new_char = char
        result.append(new_char)
    return ''.join(result)
```
