The function appears to shift the alphabet characters forward by 2 positions, wrapping around the alphabet when necessary. It leaves numbers, spaces, and special characters unchanged. The case of each letter (uppercase or lowercase) is preserved.

[CODE]: 
```python
def approx_function(s):
    result = []
    for char in s:
        if char.isalpha():
            shift = 2
            offset = 65 if char.isupper() else 97
            result.append(chr(((ord(char) - offset + shift) % 26) + offset))
        else:
            result.append(char)
    return ''.join(result)
```