The function takes a string as an input and adds 6 to the ASCII value of each character (modulo 256), except for digits and special characters which remain unchanged. 

[CODE]: 
```python
def approximate_function(s: str) -> str:
    output = ""
    for c in s:
        if c.isalpha():
            output += chr(((ord(c) - ord('A') + 6) % 26) + ord('A')) if c.isupper() else chr(((ord(c) - ord('a') + 6) % 26) + ord('a'))
        else:
            output += c
    return output
 ```
You can test this approximate function with various inputs to see if it matches the behavior of the original function.