The function takes a string input and increments the ASCII value of each alphabetic character in the input string, while keeping numbers, symbols, and non-ASCII characters unchanged.

[CODE]:
```python
def approx_function(s: str) -> str:
    result = ""
    for char in s:
        if char.isalpha():
            result += chr(((ord(char) - ord('A') + 5) % 26) + ord('A') if char.isupper() else ((ord(char) - ord('a') + 5) % 26) + ord('a'))
        else:
            result += char
    return result
```

Please note that this code is an approximation of the behavior of f(x) based on the test cases provided.