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Because the tangent function is undefined at odd multiples of π/2 (when the value of the
cosine function is zero), the graph consists of separate branches with breaks at these values. These
branches are separated by vertical asymptotes. Since we are currently graphing in connected
mode, the calculator has joined the branches resulting in the vertical line segments drawn where
the asymptotes would be. Sometimes this can be an advantage, because they can help you to
visualize where the asymptotes are. Regardless, it is important to understand that these line
segments are NOT part of the graph of the tangent function!
One way to try to avoid these line segments is to modify the window settings. If we can
create a window so that the positions of the vertical asymptotes correspond to pixel
coordinates, the "false connections" will not be drawn. This can be nearly impossible
though when the asymptotes occur at awkward values such as π/2. A second method to remove
the false connections is to graph the function in DOT style. This is accomplished using the style
setting on the function editor page. |
