The function f(x) adds 4 to the ASCII value of each alphabetical character in the input string. For non-alphabetic characters, the function doesn't change their value.

[CODE]: 
```python
def f_approx(x):
    result = ""
    for char in x:
        if char.isalpha():
            result += chr(((ord(char) - 65 + 4) % 26) + 65) if char.isupper() else chr(((ord(char) - 97 + 4) % 26) + 97)
        else:
            result += char
    return result
```