How can the built-in range function take a single argument or three?

lqc's answer demonstrates how range is implemented in C. You may still be curious about how range would be implemented if Python's built in functions were written in Python. We can read PyPy's source code to find out. From pypy/module/__builtin__/functional.py:

def range_int(space, w_x, w_y=NoneNotWrapped, w_step=1):
    """Return a list of integers in arithmetic position from start (defaults
to zero) to stop - 1 by step (defaults to 1).  Use a negative step to
get a list in decending order."""

    if w_y is None:
        w_start = space.wrap(0)
        w_stop = w_x
    else:
        w_start = w_x
        w_stop = w_y

The first argument, space, appears as an argument in all the built-in functions I saw, so I'm guessing it's kind of like self in that the user does not directly supply it. Of the remaining three arguments, two of them have default values; so you can call range with one, two, or three arguments. How each argument is interpreted depends upon how many arguments were supplied.

The beauty of open-source software is that you can just look it up in the source:

(TL;DR: yes, it uses varargs)

if (PyTuple_Size(args) <= 1) {
    if (!PyArg_UnpackTuple(args, "range", 1, 1, &stop))
        return NULL;
    stop = PyNumber_Index(stop);
    if (!stop)
        return NULL;
    start = PyLong_FromLong(0);
    if (!start) {
        Py_DECREF(stop);
        return NULL;
    }
    step = PyLong_FromLong(1);
    if (!step) {
        Py_DECREF(stop);
        Py_DECREF(start);
        return NULL;
    }
}
else {
    if (!PyArg_UnpackTuple(args, "range", 2, 3,
                           &start, &stop, &step))
        return NULL;

    /* Convert borrowed refs to owned refs */
    start = PyNumber_Index(start);
    if (!start)
        return NULL;
    stop = PyNumber_Index(stop);
    if (!stop) {
        Py_DECREF(start);
        return NULL;
    }
    step = validate_step(step);    /* Caution, this can clear exceptions */
    if (!step) {
        Py_DECREF(start);
        Py_DECREF(stop);
        return NULL;
    }
}

Range takes, 1, 2, or 3 arguments. This could be implemented with def range(*args), and explicit code to raise an exception when it gets 0 or more than 3 arguments.

It couldn't be implemented with default arguments because you can't have a non-default after a default, e.g. def range(start=0, stop, step=1). This is essentially because python has to figure out what each call means, so if you were to call with two arguments, python would need some rule to figure out which default argument you were overriding. Instead of having such a rule, it's simply not allowed.

If you did want to use default arguments you could do something like: def range(start=0, stop=object(), step=1) and have an explicit check on the type of stop.