The function takes a single character as input and, if it's a lowercase or uppercase letter, it adds 9 to its ASCII value, wrapping from 'z'/'Z' back to 'a'/'A'. Numerical characters are ignored, and special characters remain unchanged.

[CODE]: Here is a Python code implementation that mimics the behavior of the function:

```python
def approximate_function(input_string):
    output_string = ""
    for character in input_string:
        if (65 <= ord(character) <= 90) or (97 <= ord(character) <= 122):
            new_character = chr((ord(character) + 9 - 65) % 26 + 65) if character.isupper() else chr((ord(character) + 9 - 97) % 26 + 97)
            output_string += new_character
        elif not character.isdigit():
            output_string += character
    return output_string
```