# 13.1: Inverse Variation

*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 column in and the column in as shown.

1 | |

2 | |

3 | |

4 | |

5 | |

6 |

Press , and select **Plot1**.

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

Press **WINDOW**. Set the window to the following:

Press **GRAPH**.

## Part 2 - Questions

- How would you describe the relationship between and 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 . Enter a formula to multiply the entries in by the entries in . Press for and press for .

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

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

Solve the equation for . Press . Enter the equation into .

- 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 **[TABLE]** to examine the function table.

- What is happening when ? Why?

Arrow up to the negative values in the table.

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

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

Press **GRAPH**.

- What appears to be happening when ?
- 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.