The function seems to be incrementing the odd-indexed characters in the input string by 2 and the even-indexed characters by 24. Characters that are not part of the alphabet are left unchanged. Note that indexing starts at 0.

[CODE]:
def approximated_function(input_string):
    output_string = ""
    for i, char in enumerate(input_string):
        if char.isalpha():
            increment = 2 if i % 2 == 0 else 24
            new_char = chr(((ord(char) - ord('a') + increment) % 26) + ord('a'))
        else:
            new_char = char
        output_string += new_char
    return output_string