The function seems to replace all occurrences of the letter "b" in the input string with the letter "v".

[CODE]:
```python
def approx_function(input_string):
    return input_string.replace('b', 'v')
```

Let's test a few more inputs to make sure the approximation holds. 

COMMAND: PYTHON(./temp/function.py "bobcat" "batman" "rabbit" "foobar")