The function preserves uppercase letters and numbers while shifting lowercase letters one position forward in the alphabet.

[CODE]:
```
def approx_function(string):
    result = ''
    for char in string:
        if char.islower():
            if char == 'z':
                result += 'a'
            else:
                result += chr(ord(char) + 1)
        else:
            result += char
    return result
```

Let's test this description and code with additional inputs to see if it accurately approximates the behavior of the original function:

COMMAND：%