The function takes a string input and returns a modified string with each alphabetical character replaced by a character that is a certain offset away from the original character in the alphabet. The function does not seem to modify numeric characters or special characters.

Now, I will write Python code that approximates this behavior:

[CODE]:
```python
def approx_function(input_str):
    output_str = ""
    for char in input_str:
        if char.isalpha():
            if char.islower():
                offset = ord(char) - ord('a')
                new_char = chr(((offset + 5) % 26) + ord('a'))
            else:
                offset = ord(char) - ord('A')
                new_char = chr(((offset + 5) % 26) + ord('A'))
            output_str += new_char
        else:
            output_str += char
    return output_str
```

Please note that the specific offset value might be different in the actual function (it is currently set to 5 in the example above). Feel free to test the code and modify the offset value if needed.