It crosses the horizontal asymptote when it should not

The angle between which two asymptotes?

The vertical line is called an asymptote, it is not connecting the graph, it means that the function goes to infinity as the function nears the line. In this case the graph goes to infinity and negative infinity as the x nears 7. This is because the function becomes undefined at x = 7 , plug 7 into x and we get 1/0, dividing by zero is undefined. Thus, the calculator puts the vertical asymptote in the graph to symbolize the action of the function nearing infinity.

Press MODE and change "Connected" to "Dot".

Alternatively, you can change the style for individual graphs. In the Y= screen, move to the line then press left-arrow to move past the = sign, then press ENTER repeatedly to cycle through the different graph styles.

I have drawn the curve for your function. On my TI84Plus with OS version 2.53MP the spurious asymptotes do not show, while on a TI83PLUS OS 1.12 they do if the graph is drawn as connected lines. It might be a bug that was corrected in newer OS (for TI84PLUS)



The graph from a TI83PLUS (the last one above) shows asymptotes when drawn connected, but no asymptotes appear if graph is drawn dotted.
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The asymptote you see is in truth a spurious effect. It appears when you draw connected graphs. There is no command that turns that "non-existing feature" ON and OFF.
If you do not want to see the "asymptote" draw dotted graphs. The drawback is that you will have fewer points near the asymptote because the curve grows too fast. If you decrease the x-step to have more points, the graph will take longer and you may run out of RAM.

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 asymptote is thus connected to the first 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.

Here is a function that will "show" you a vertical asymptote on the TI84PLus, when graph is drawn connected, but on a calculator with a higher resolution, you see none. A calculator cannot handle infinity. You can with the help of your mind's sight, so to speak, see the asymptote on the graph.

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.

Hello,
I have answered this question multiple times. I have no idea why you calculator refuses to allow you to choose more graph styles. Maybe you should reset it by clearing the RAM.
Concerning the connected asymptotes.
In truth your function has one aymptote namely the straight line x=2 but your graph has two asymptotic branches, one tends towards -infinity, the other toward + infinity. That they seem connected is an illusion due to the finite resolution of the screen. This is made worse if you select a connected graph instead of a dotted one. I am enclosing a screen capture of the graph for the same function, drawn on a calculator with better resolution.



This clarification being given, it remains that you still have a problem since you cannot choose other styles. Do try to reset the RAM, and choose dotted graphs. If that does not work, maybe you should update the OS or reinstall it from education.ti.com.
I hope it solves your problem. If it does not, do not blame me, and remember that I tried my best.

The calculator can't tell the difference between a function with an aymptote and a function that rapidly goes from a large positive number to a large negative number in one step.

One way around this is to plot with the asymptote at one edge. Press the WINDOW key and change the limits. Another way is to change the plot type from Line to Dots. Press Y= to enter the Y= editor, select the function being plotted, press Left to highlight the = sign, then press ENTER repeatedly to cycle through the different graph styles.

I have a similar symptom, that is, apparent loss of scroll ring functionality as homercles1 noted, but in fact the scroll ring functionality gets toggled between horizontal scrolling and vertical scrolling as Rithas has noted. A window that is not wide enough to require horizontal scrolling will give the appearance of loss of scroll ring functionality when the scroll ring is in horizontal scroll mode. Likewise, a window that is not tall enough to require vertical scrolling will give the appearance of loss of scroll ring functionality when the scroll ring is in vertical scroll mode.
Solution that worked for me:
My upper right-hand button is defined as "Allow Horizontal Scroll" and by clicking this button, the scroll ring function toggles between horizontal and vertical scrolling. In fact, what can appear to be a nonfunctional scroll ring in some windows is very useful when moving around in large windows.
Hope this comment will be useful to you.