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Session 2, Part C:
Examining Zero
In This Part: The Behavior of Zero | Positional Number Systems
Exploring Zero and Infinity on a Graph
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We can further explore the number line and its elements through a graphic representation of an equation. For example, on such a graph we can visually locate an irrational number or demonstrate what happens when we try to divide with 0.
Let's explore the graph of the equation x • y = 12.
Use the Interactive Activity to explore this graph. Answer Problems C3-C8 and corroborate your answers on the graph.
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. For a non-interactive version of this activity, examine the graph below and answer Problems C3-C8.
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Here is the graph of the equation x • y = 12 in the first quadrant:
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Problem C3 |  |
a. | Would the point (2,6) be on the graph? How do you know? |
b. | What about the point (24,0.5)? |
c. | What about the point (-3,4)? |
d. | Experiment with putting different numbers from the number line into the equation. What happens? |
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Problem C4 | |
What y value would be paired with x = 4? How do you know? |
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Problem C5 | |
a. | What is the significance of the point of intersection of this graph and the line y = x? |
b. | Estimate the coordinates of this point. |
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Problem C6 | |
Will the graph ever touch either the x- or y-axis? Explain. |
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Problem C7 | |
What happens on the graph when x = 0 or y = 0? How does this demonstrate why you cannot divide a number by 0? |
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Problem C8 | |
Using the Interactive Activity, switch to the four-quadrant version of the graph. Now try plotting points for x = -0.5, x = -1, and x = -4. Does this view change your answer to Problem C5?
For a non-interactive version of this problem, look at the graph of x • y = 12 above. This graph shows only the first quadrant. Would there be points in any other quadrant? Does this change your answer to Problem C5? Explain.
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