Exploring Inverse Variation

How does the graph look when a is positive?
How does the graph look when a is negative?
What happens to y as x increases?
What happens to y as x decreases?
How does the product of xy relate to a?
What is the equation for inverse variation?
The following questions have to do with the scenario stated below.
The amount of heat lost through a windowpane depends on how thick the glass is. A formula for this function for a certain window is[br][math]y=\frac{12}{x}[/math][br]in which x represents the thickness of the pane in millimeters and y represents the number of units of heat lost.[br][br]In your notebook:[br][br]1. Copy and complete the following table[br][img]data:image/png;base64,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[/img][br][br][br]2. Graph the function.
What happens to the units of heat lost, y, as the thickness in millimeters, x, increases?
How do the thickness and units of heat lost vary with each other?
As one of the two variables in this function becomes very large, what happens to the other?
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Information: Exploring Inverse Variation