The function appears to modify the input string by shifting certain characters to either the preceeding or the succeeding character in the alphabet. It also seems to leave some characters unchanged. However, the position or specific type of characters being altered appears inconsistent.

[CODE]: 
```python
def approximate_function(input_string):
    output = ""
    for i, char in enumerate(input_string):
        if char.isalpha():
            if i % 2 == 0:
                if char.lower() == 'z':
                    output += 'a' if char.islower() else 'A'
                else:
                    output += chr(ord(char) + 1)
            elif i % 2 == 1:
                if char.lower() == 'a':
                    output += 'z' if char.islower() else 'Z'
                else:
                    output += chr(ord(char) - 1)
        else:
            output += char
    return output
```
Keep in mind that this code is an approximation and may not fully represent all aspects of the original function.