The function inserts "U" after the second character of the input string and replaces the first character with its subsequent ASCII value.
[CODE]:
```python
def approximate_function(input_string):
    if len(input_string) < 1:
        return ""

    first_char = input_string[0]
    subsequent_char = chr(ord(first_char) + 1)

    modified_string = input_string[1:2] + "U" + input_string[2:]
    return subsequent_char + modified_string
```
Let's test this code with a few more inputs to confirm our understanding of the function.

COMMAND: PYTHON(./temp/function.py "hello123" "test" "Python")