The function adds the character 't' after the second character of the input string. If the input string has only one character, the 't' is added at the end of the string.

[CODE]:
```python
def approx_function(s):
    if len(s) == 1:
        return s + 't'
    else:
        return s[:2] + 't' + s[2:]
```

To make sure this is a good approximation, let's test the function again with a new set of inputs.

COMMAND: PYTHON(./temp/function.py "Quick" "brown" "fox")