The function shifts each alphabetic character in the input string by 14 positions forward in the alphabet, wrapping around from 'z' to 'a', and from 'Z' to 'A'. The case of the characters is preserved (i.e., uppercase remains uppercase and lowercase remains lowercase), and non-alphabetic characters are left unchanged.

[CODE]: 
```python
def approximate_function(input_string):
    output = ""
    for char in input_string:
        if char.isalpha():
            shift = 14
            if char.isupper():
                output += chr((((ord(char) - ord('A')) + shift) % 26) + ord('A'))
            else:
                output += chr((((ord(char) - ord('a')) + shift) % 26) + ord('a'))
        else:
            output += char
    return output
```