The function shifts alphabetical characters while leaving digits and special characters unchanged. Both upper and lower case characters are transformed in the same way.

[CODE]:
```python
def shift_character(c: str) -> str:
    if c.isalpha():
        shifted = (ord(c.lower()) - ord("a") + 21) % 26
        return chr(shifted + ord("a"))
    else:
        return c

def approx_function(x: str) -> str:
    return "".join([shift_character(c) for c in x])
```

This code assumes the function shifts characters by 21 positions. The shifting pattern may differ, so I encourage further testing and adaptation of the code.