| KU Interactive Mathematics |
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This example will show you that the screen resolution of a graphing calculator has some limitations, and that we need to interpret what is displayed with a solid mathematical understanding of the functions we are graphing.
| What to Enter | Screen Shots |
Let’s graph y1 = x2 and y2 = x4 simultaneously. |
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| Use ZOOM and make a zoom box like this: Then, hit ENTER. |
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| Observe the following: Between x = –1 and x = 1, y1 = x2 is above y2 = x4. For x < –1 and x > 1, y1 = x2 is below y2 = x4. Check this by evaluating the functions at a few points. |
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| Now, graph y = x20. Notice that this graph rises much sharper than the previous two when x < –1 and x > 1 and that it is flatter between x = –1 and x = 1. Why is that? Again, numerically evaluate the function at a few points and see why the graph should look like it does here. |
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| Finally, graph y = x22. Then, the screen shot looks like this: It is apparent that the display cannot show the difference between the graphs of y = x20 and y = x22. So, do we give up on graphing these two? |
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If we recall what we did earlier in this example, we can deduce that the relative locations of the graphs of y = x20 and y = x22 should remain the same as were for the graphs of y1 = x2 and y2 = x4. |
It is great that we have access to tools like TI-83/84/89. But, in the end, it is our understanding of the underlying mathematics that makes these tools useful to us. |
| So, if we are asked to graph y = x20 and y = x22, we will simply draw graphs like these on the right and name them as such. Anyone can see that we have made the point by showing the relative locations of the graphs corresponding to the value of x. | |
| Course Info | Office Hours | Exams | LiveMath | TI | Help | |
KU | Math Dept | Home |
| KU Interactive Mathematics |
Disclaimer • Updated September 4, 2008
Email: mitsuma@kutztown.edu
Phone: +1 (610) 462-WPJW
Phone: +1 (610) 462-WPJW