The function replaces the last letter of the input string with the next letter in the alphabet (wrapping from 'z' to 'a') and then appends an 'N' to the end.

[CODE]:
```python
def approximate_function(input_string):
    last_letter = input_string[-1]
    new_last_letter = chr(((ord(last_letter) - ord('a') + 1) % 26) + ord('a'))
    return input_string[:-1] + new_last_letter + 'N'
```