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A comprehensive graph of a rational function should show all intercepts, all
relative maxima or minima (turning points), and all asymptotic behavior (including
any points where the graph intersects an asymptote). With this example, a standard
graph seems to meet all the criteria.
However, there are some other issues concerning this graph. First
of all, the actual graph consists of three separate branches
that the TI-83/84 has artificially connected. These branches are separated
by vertical asymptotes at the values x = -1.5 and x
= 2. Because 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 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, these "false connections" will not be
drawn. This can be tricky to manage though! |
