The function appears to take a string input and for alphabetic characters, it shifts each character by two positions forward in the alphabet, regardless of the letter's case (upper or lower). For non-alphabetic characters (such as digits and symbols), it leaves them unchanged.

[CODE]: 

```python
def approximate_function(input_string):
    output_string = ""
    for char in input_string:
        if char.isalpha():
            shift = 2
            if char.islower():
                output_string += chr(((ord(char) - ord('a') + shift) % 26) + ord('a'))
            elif char.isupper():
                output_string += chr(((ord(char) - ord('A') + shift) % 26) + ord('A'))
        else:
            output_string += char
    return output_string
```