If the length of the input string is even, it swaps the 2nd and 2nd-last letters. Otherwise, the input string remains unchanged.

[CODE]:
```python
def approximation_function(s):
    if len(s) % 2 == 0:
        s = list(s)
        s[1], s[-2] = s[-2], s[1]
        return "".join(s)
    else:
        return s
```

Now, let's test this function on a few more inputs to better understand its behavior.

COMMAND: PYTHON(./temp/function.py "banana" "computer" "science" "qwerty" "abcdef")