The function adds 2 to the ASCII value of each character, preserving 'x' and 'X' without change. It wraps around 'z' to 'a' and 'Z' to 'A' after adding 2.

[CODE]: 
```
def approx_function(s: str) -> str:
    result = ''
    for ch in s:
        if ch == 'x' or ch == 'X':
            result += ch
        elif ch in 'abcdefghijklmnopqrstuvwyz':
            result += chr(((ord(ch) - ord('a') + 2) % 26) + ord('a'))
        elif ch in 'ABCDEFGHIJKLMNOPQRSTUVWYZ':
            result += chr(((ord(ch) - ord('A') + 2) % 26) + ord('A'))
        else:
            result += ch
    return result
```

Please let me know if there is anything else you'd like me to do.