The function shifts the alphabet characters in the input string by a certain number of positions, reverse the order of digits, and special characters. The letter case is preserved.

[CODE]: 
```python
def approximate_function(s: str) -> str:
    shifted = []
    for c in s:
        if c.isalpha():
            shift = 3 if c.islower() else -3
            shifted_char = chr(((ord(c) - ord('a' if c.islower() else 'A') + shift) % 26) + ord('a' if c.islower() else 'A'))
            shifted.append(shifted_char)
        elif c.isdigit():
            shifted.append(c[::-1])
        else:
            shifted.append(c[::-1])

    return ''.join(shifted)
```
Keep in mind that this is just an approximation of the actual function based on the provided test examples.