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# 13.1: Inverse Variation

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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?

• 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 $2^{nd}\ [L1]$ for $L1$ and press $2^{nd}\ [L2]$ for $L2$. $L3 = L1*L2$

Press ENTER to execute the formula. The product in each case is $24$. So, $L1 \cdot L2 = 24$ or $x \cdot y = 24$. 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 $x \cdot y = 24$ for $y$. Press $Y=$. Enter the equation into $Y1$.

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 $2^{nd}$ [TABLE] to examine the function table.

• What is happening when $x = 0$? Why?

Arrow up to the negative $x-$values in the table.

• What do you notice about the $y-$values?
• Why does this occur?
• What do you think the graph of your equation looks like to the left of the $y-$axis?

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.

Feb 22, 2012

Aug 19, 2014