The function takes a string input, and for every second character, it increases the ASCII code by 1. If the increased ASCII code goes beyond 'z', then it will wrap back to 'a'.

[CODE]: 
```python
def approx_f(x):
    result = []
    for i, char in enumerate(x):
        if i % 2 == 1:
            ascii_code = ord(char)
            if ascii_code == 122:  # 'z'
                ascii_code = 97   # 'a'
            else:
                ascii_code += 1
            result.append(chr(ascii_code))
        else:
            result.append(char)
    return ''.join(result)
```

Now, I will run more tests to confirm the behavior.

COMMAND: PYTHON(./temp/function.py "Zigzag" "XYZ" "Success" "TestingCode" "Palindrome")