How to Determine the Accuracy of TI83 Plus Graphs
The TI83 Plus graphing calculator can do only what you tell it to do — which doesn’t always produce an accurate graph. The three main causes of inaccurate graphs, and their solutions, are the following:

The graph is distorted by the size of the screen.
Because the calculator screen isn’t square, circles don’t look like circles unless the viewing window is properly set. How do you properly set the viewing window? No problem! Just graph the function and then press [ZOOM][5] to invoke the ZSquare command. ZSquare readjusts the window settings for you and regraphs the function in a viewing window in which circles look like circles.

The viewing window is too small or too big.
If you don’t know what the graph should look like, then after graphing it you should zoom out to see more of the graph or zoom in to see a smaller portion of the graph. To do this, press [ZOOM][3] to zoom out, or press [ZOOM][2] to zoom in.
Then use the
keys to move the cursor to the point from which you want to zoom out or in, and press [ENTER]. It’s just like using a camera. The point you want to move the cursor to is the focal point.
After zooming in or out, you may have to adjust the window settings.

Vertical asymptotes may not be recognizable.
In all graph styles except Animate and Dotted Line, the calculator graphs one point, and then the next point, and connects those two points with a line segment. This sometimes causes vertical asymptotes to appear on the graph.
In a different viewing window, the vertical asymptote may not even appear. This happens when the calculator graphs one point, but the next point is undefined because the x value of that point is exactly at the location of the vertical asymptote.