The function f(x) shifts each alphabetical letter in the input string forward by one position in the alphabet while keeping other characters unchanged.

[CODE]:
```python
def approximate_function(input_str):
    output_str = ""
    for char in input_str:
        if char.isalpha():
            new_char = chr(((ord(char) - 65 + 1) % 26) + 65) if char.isupper() else chr(((ord(char) - 97 + 1) % 26) + 97)
            output_str += new_char
        else:
            output_str += char
    return output_str
```