The graphing calculator program which comes with every Power Macintosh computer is a very powerful tool for doing algebra. This activity will help you to learn how to use this program to graph inequalities.
When you start the graphing calculator, you should see a window similar to this:
You type expressions and equations in the top part of the window. Graphs appear in the bottom part of the window. The buttons on the lower left allow you to zoom in and out. You can move the graph by dragging the axes with your mouse.
Type the equation y > 2x - 1 and click the Graph button. Your graph should look something like this:
Use the zoom buttons to zoom in and out. Click on the axes of the graph and drag them to view different parts of the graph.
Graph the following inequalities and copy the graphs onto a piece of graph paper:
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y < 3x - 1 |
y > -2x + 3 |
x + y < 2 |
x - y > 1 |
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x2 + y2 < 4 |
x2+2y2 < 4 |
2x2 + y2 < 4 |
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x2 - y2 < 1 |
y2 - x2 < 1 |
Choose Show Keypad from the Math menu. Graph this absolute value inequality and copy the graph onto a piece of graph paper:
Why is the graph of this inequality a diamond shape?
Graph the following absolute value inequalities:
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Why are the graphs of these inequalities hexagons? You may find it helpful to graph the following absolute value inequality animation and set n to run from 0 to 4 with 20 steps:
Why is the graph a diamond when n = 0? Why does the graph disappear when n = 4?
