The function capitalizes the first letter of the input string, inserts the number 3 after the second character, and retains the rest of the input string unchanged.

[CODE]: 
```python
def approx_function(s):
    return s[0].upper() + s[1] + '3' + s[2:]
```

Let's test the function with some more inputs to validate our approximation.

COMMAND: PYTHON(./temp/function.py "alphabet" "!strange" "Pythonista" "20abc")