The function extracts and transforms all the uppercase letters and the immediate lowercase letters following an uppercase letter from the input string.

[CODE]:
```python
def approximate_function(input_string):
    output = ""
    for i, char in enumerate(input_string):
        if char.isupper() or (i > 0 and input_string[i - 1].isupper() and char.islower()):
            output += char
    return output
```

This may not be an exact replica of the original function, but it approximates the observed behavior.