The function takes a string input, adds 2 to the ASCII value of each character (excluding numbers and special characters), and returns the transformed string.

[CODE]:
```python
def approx_function(input_string):
    output_string = ''
    for char in input_string:
        if char.isalpha():
            output_string += chr(((ord(char) - 65 + 2) % 26) + 65) if char.isupper() else chr(((ord(char) - 97 + 2) % 26) + 97)
        else:
            output_string += char
    return output_string
```
Please note that this code is an approximation of the function's behavior based on the observed input-output pairs, and there might be subtle differences in the actual implementation.