The function increments the last alphabetic character of the input string by one. If the input string consists of only numeric characters, an empty output is returned.

[CODE]:
```python
def approximate_function(input_string):
    if not any(c.isalpha() for c in input_string):
        return ""
    for i in reversed(range(len(input_string))):
        if input_string[i].isalpha():
            incremented_char = chr(ord(input_string[i]) + 1)
            return input_string[:i] + incremented_char
    return input_string
```

Keep in mind that this is an approximation of the function, and there might be additional behaviors not accounted for by this code snippet.