The function capitalizes the first letter of the input string and then alternates the case of each character.

[CODE]:
```python
def alternate_case(s):
    result = []
    upper = True
    for char in s:
        result.append(char.upper() if upper else char.lower())
        upper = not upper
    return ''.join(result)
```

You can try running this code on other inputs to further validate its behavior.