How do I turn off the vertical asymptote feature?

Hello,
There is no vertical (or otherwise) asymptote feature on a TI84PLUS. It seems to you that the calculator is drawing the asymptote. However when you plot a CONNECTED Graph a line is drawn from one point to the next: The last point on one side of the asymptopte is thus connected to the fisrt point on the other side, effectively mimicking the drawing of the asymptote.
To get rid of this spurious effect, draw dotted graphs, but you will see fewer points, because the points are drawn at constant intervals in X. This is set by the Xres variable, in the Window configuration screen.

Hope it helps.