The function takes a string input and shifts each alphabetic character by a fixed amount. It leaves numbers and special characters unchanged.

[CODE]:
```python
def approx_function(input_str):
    shift_amt = 24  # It appears that the letters are being shifted by 24 positions
    output = ''
    for char in input_str:
        if char.isalpha():
            if char.islower():
                output += chr(((ord(char) - ord('a') + shift_amt) % 26) + ord('a'))
            else:
                output += chr(((ord(char) - ord('A') + shift_amt) % 26) + ord('A'))
        else:
            output += char
    return output
```

Let's try some additional inputs to confirm our description and code.

COMMAND: PYTHON(./temp/function.py "world" "Shift24" "Zebra1!")