The function rotates uppercase ASCII characters to the right by one position and maps lowercase letters to the uppercase characters rotated to the right by one position starting from 'b'. It leaves digits and special characters unchanged.

[CODE]:
```python
def approximate_function(s):
    result = ""
    for char in s:
        if char.isupper():
            result += chr(((ord(char) - 65 + 1) % 26) + 65)
        elif char.islower():
            result += chr(((ord(char.upper()) - 65 + 1 + ord('B') - ord('A')) % 26) + 65)
        else:
            result += char
    return result
```