The function takes an input string and replaces lowercase alphabets with corresponding characters three positions later in the alphabet (wraps around after z) and leaves all other characters unchanged.

[CODE]:
```python
def approximate_function(input_string):
    output_string = ""
    for char in input_string:
        if char.islower():
            output_string += chr(((ord(char) - ord('a') + 3) % 26) + ord('a'))
        else:
            output_string += char
    return output_string
```
This Python code approximates the behavior of the given function.