The function capitalizes the first letter of the input string and transforms the second character according to a specific rule (e->G, i->N, o->Q, u->W).

[CODE]:
```python
def approx_function(s):
    s = s.capitalize()
    if len(s) > 1:
        if s[1] == 'e':
            s = s[0] + 'G' + s[2:]
        elif s[1] == 'i':
            s = s[0] + 'N' + s[2:]
        elif s[1] == 'o':
            s = s[0] + 'Q' + s[2:]
        elif s[1] == 'u':
            s = s[0] + 'W' + s[2:]
    return s
```