The function shifts each character in the input string by 13 positions in the alphabet (case-sensitive) and keeps the digits unchanged.
[CODE]:
```python
def f_approx(x):
    result = []
    for char in x:
        if char.isalpha():
            shift = 13
            char_code = ord(char)
            if char.islower():
                result.append(chr((char_code - ord('a') + shift) % 26 + ord('a')))
            elif char.isupper():
                result.append(chr((char_code - ord('A') + shift) % 26 + ord('A')))
        elif char.isdigit():
            result.append(char)
    return ''.join(result)
```