The function takes a string input and adds 16 (in hexadecimal) to its ASCII value of the first character, leaving the other characters unchanged.

[CODE]:
```python
def approx_function(input_str):
    if input_str:
        first_char_ascii = ord(input_str[0])
        altered_first_char = chr(first_char_ascii + 0x10)
        output_str = altered_first_char + input_str[1:]
        return output_str
    else:
        return ''
```
