The function takes a string input and adds 1 to the ASCII value of every even-indexed character (0-based index), while keeping the odd-indexed characters the same.

[CODE]: 

```python
def approximate_function(input_string):
    output_string = ""
    for index, character in enumerate(input_string):
        if index % 2 == 0:
            output_string += chr(ord(character) + 1)
        else:
            output_string += character
    return output_string
```

To validate the description and code, let's test some more inputs.

COMMAND: PYTHON(./temp/function.py "validation" "example" "BlueForest" "algorithm" "challenge")