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13.1: Inverse Variation

Difficulty Level: At Grade Created by: CK-12
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This activity is intended to supplement Algebra I, Chapter 12, Lesson 1.

Part 1 - Enter the Data

Enter the data from the table into lists.

Press STAT ENTER. Enter the x column in L1 and the y column in L2 as shown.

x y
1 24
2 12
3 8
4 6
5 4.8
6 4

Press Y=, and select Plot1.

Press ENTER to turn the plot On. Select scatter as the type of plot, L1 for the Xlist, and L2 for the Ylist.

Press WINDOW. Set the window to the following:

Xmin=0, Xmax=10, Xscl=2

Ymin=0, Ymax=25, Yscl=5

Press GRAPH.

Part 2 - Questions

  • How would you describe the relationship between x and y by examining this data?

Press STAT ENTER to return to the lists.

  • What relationships can you see by examining the numbers in the lists?
  • What is the product of each pair of numbers?

Arrow to the top of L3. Enter a formula to multiply the entries in L1 by the entries in L2. Press 2nd [L1] for L1 and press 2nd [L2] for L2. L3=L1L2

Press ENTER to execute the formula. The product in each case is 24. So, L1L2=24 or xy=24. This relationship, when x and y have a constant product, is called “inverse variation.”

  • What type of situation might this be a formula for?

Solve the equation xy=24 for y. Press Y=. Enter the equation into Y1.

  • What is your equation?

Press GRAPH.

  • What other information can you find from the graph of the equation that you could not gather from the plot?
  • Does this graph appear to be a function? Explain.

Press 2nd [TABLE] to examine the function table.

  • What is happening when x=0? Why?

Arrow up to the negative xvalues in the table.

  • What do you notice about the yvalues?
  • Why does this occur?
  • What do you think the graph of your equation looks like to the left of the yaxis?

Press WINDOW. Set the window as shown to examine the graph when x is negative.

Press GRAPH.

  • What appears to be happening when x=0?
  • Why does the graph of the equation not appear in Quadrants II or IV?
  • Do you think an inverse variation can ever be found in Quadrants II or IV? Why?
  • Does this graph appear to be a function now? Explain.

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Date Created:
Feb 22, 2012
Last Modified:
Oct 31, 2014
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