Currently it only supports functions that have no holes or gaps or anything. Thus, graphing $$y=|\sqrt x|$$ gives $$y=\begin{cases} 0 & \text{if } x<0 \\ |\sqrt x| & \text{if } x\ge0 \end{cases}$$.

Edit: Fixed it!

How does it graph the tangent example without drawing vertical lines at the poles?

I honestly don't know. I was surprised at that, too.

Edit: If you change the step to, say, 1, you do indeed get them.

Ah. You could probably catch that case (previous value was huge and new value is huge in the other direction).

My brain is currently too tired to think of how to do so.

Good night!

Is that because you're going to sleep, or that I implied I would?

That was what I meant, although I'm going to bed pretty soon too.