The function f(x) takes a string input and modifies only the last character of the string by adding 6 to its ASCII value. If the modified ASCII value exceeds the original range (lowercase, uppercase, etc.), it wraps around within the same range.

[CODE]: 
```python
def approx_function(s: str) -> str:
    last_char = s[-1]
    if 'a' <= last_char <= 'z':
        new_last_char = chr(((ord(last_char) - ord('a') + 6) % 26) + ord('a'))
    elif 'A' <= last_char <= 'Z':
        new_last_char = chr(((ord(last_char) - ord('A') + 6) % 26) + ord('A'))
    else:
        new_last_char = chr(ord(last_char) + 6)
    return s[:-1] + new_last_char
```