Graph the equation with the help of graphing calculator
Write a short essay describing different ways in which a graphing calculator might give a misleading graph of an equation.
A graphing calculator displays a rectangular portion of the graph of an equation in a display window or viewing screen, which we call a viewing rectangle. The default screen often gives an incomplete or misleading picture, so it is important to coose the viewing rectangle with care.
Let us graph the equation with different viewing rectangles. We start with the viewing rectangle . The resulting graph as shown below is blank.
This is because for all ,
Hence, the graph lies entirely above the viewing rectangle, so this viewing rectangle is not appropriate.
If we enlarge the viewing rectangle to , as illustrated below, we begin to see a portion of the graph.
If we enlarge the viewing rectangle to , the graph seems to be more complete.
Further enlarging the viewing rectangle, the graph do not show the intercept is .
Hence, the viewing rectangle to is an appropriate representation of the graph.
Now graph the equations together in the viewing rectangle . The graphs are so shown below.
One is a parabola, while the other is a line. It seems as if the graphs intersect near the point .
Hence, if we zoom in on the area around this point as illustrated below, we see that although the graphs almost touch, but they do not actually intersect.
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