The function appears to shift each alphabetic character in the input string. Uppercase letters are shifted +1 (e.g., A -> B), and lowercase letters are shifted +5 (e.g., a -> f). Digits and special characters remain unchanged.

[CODE]: 
```python
def approx_function(input_string):
    output = ""
    for char in input_string:
        if char.isalpha():
            if char.isupper():
                output += chr(((ord(char) - ord('A') + 1) % 26) + ord('A'))
            else:
                output += chr(((ord(char) - ord('a') + 5) % 26) + ord('a'))
        else:
            output += char
    return output
```