The function replaces the first character with its next character in the alphabet, replaces "a" with "B", "f" with "j", and converts capital letters to lower-case without additional changes.

[CODE]:
```python
def approximate_function(s):
    s = s.lower()
    s = chr(((ord(s[0]) - ord('a') + 1) % 26) + ord('a')) + s[1:]
    s = s.replace("a", "B")
    s = s.replace("f", "j")
    return s
```
Please note that this code may not be perfect, but it should give a good approximation of the behavior of the function in question.