The function applies a Caesar cipher with a shift of 9 to the input string, keeping the case of the characters intact.

[CODE]:
```python
def approx_function(s):
    result = []
    for char in s:
        if 'a' <= char <= 'z':
            shifted = chr(((ord(char) - ord('a') + 9) % 26) + ord('a'))
        elif 'A' <= char <= 'Z':
            shifted = chr(((ord(char) - ord('A') + 9) % 26) + ord('A'))
        else:
            shifted = char
        result.append(shifted)
    return ''.join(result)
```