## Math Forum - Problem of the Week

### Graph Zooming

Please keep in mind that this is a research project, and there may sometimes be glitches with the interactive software. Please let us know of any problems you encounter, and include the computer operating system, the browser and version you're using, and what kind of connection you have (dial-up modem, T1, cable).

## Welcome to ZOOM!

Your challenge is to explore the concept of scale in mathematics and apply it to your everyday experiences. Scale is an important concept to mathematicians and people in many other fields, because it allows one to gain many different perspectives on the same thing. You may notice important things in one scale that you might not see in another.

### To Do and Notice

Use the graph zooming applet to experiment with different scales of a graph.

Notice what you see and don't see depending on the view you choose. Use your experiences with the applet to answer the following questions:

1. What is the point of intersection of the red and green lines? (Please write as an ordered pair.)

Zoom in so you cannot see the red line. You have just changed the scale of the graph. Notice that the minimum and maximum x and y values of the graph have changed.

2. Describe what the Zoom In button does. Why does it make the red line disappear? (Hint: Consider what points are on the red line.)

3. Suppose you could add a fourth Zoom button that would show the intersection of the green line on the y-axis (the "y-intercept"), but not show the red line at all. What would your new button do? (Hint: What would the new scale of the graph be?)

4. Bonus question: Change the equation for the blue line. Experiment with different equations until you can see your new line when the graph is in the Zoomed In position. What is the equation of your line?

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