The function takes an input string and returns a new string where all alphabetical characters are shifted right by 8 positions (circularly) in the alphabet while retaining their case. Non-alphabetic characters, such as numbers and spaces, remain unchanged.

[CODE]: 
```python
def f_x(input_string):
    output_string = ""
    for char in input_string:
        if char.isalpha():
            shift = 8
            if char.islower():
                output_string += chr(((ord(char)-ord('a')+shift)%26)+ord('a'))
            else:
                output_string += chr(((ord(char)-ord('A')+shift)%26)+ord('A'))
        else:
            output_string += char
    return output_string
```

I hope you find this description satisfactory for the function implemented in `./temp/function.py`.