The function seems to be replacing the last character of the input string with the ASCII character that is two positions after the original last character. In addition, the function appends the ASCII character that is two positions before the original last character to the end of the string.

[CODE]:
```python
def approximated_function(input_string):
    if len(input_string) > 0:
        last_char = input_string[-1]
        new_last_char = chr(ord(last_char) + 2)
        appended_char = chr(ord(last_char) - 2)
        return input_string[:-1] + new_last_char + appended_char
    else:
        return input_string
```