The function takes a string as input and adds '7' in the middle of the string. It also repeats the last character of the string once.

[CODE]: 
```python
def approx_function(s):
    mid = len(s) // 2
    return s[:mid] + '7' + s[mid:] + s[-1]
```

To validate if the approximation is correct, let's run some more tests.

COMMAND: PYTHON(./temp/function.py "example" "function" "more" "tests" "validation")