The function takes an input string, and changes the first character of that string to the next 4th letter in the alphabet. If there is no letter after the 4th letter, it wraps around the the alphabet. 

[CODE]:
```python
def approx_function(s):
    if s == "":
        return ""
    first_letter = s[0]
    updated_letter = chr(((ord(first_letter) - ord('a') + 4) % 26) + ord('a'))
    return updated_letter + s[1:]

```