The function takes an input string and shifts each alphabetic character by -1. All other characters (e.g., digits, punctuation marks) remain the same.

[CODE]: 

```python
def approx_function(s: str) -> str:
    result = []
    for char in s:
        if char.isalpha():
            offset = 1 if char.islower() else -1
            result.append(chr(ord(char) - offset))
        else:
            result.append(char)
    return ''.join(result)
```

Note: The code provided above is an approximation of the behavior of the original function based on the tested inputs.