This activity is intended to supplement Algebra I, Chapter 12, Lesson 1.
Time required: 30 minutes
Students will examine a set of ordered pairs that vary inversely. They will plot the ordered pairs and explore the graph and table for relationships. Students will also graph the inverse variation and determine whether it is a function.
Topic: Rational Functions & Equations
Given the values of two variables that vary inversely, determine the rational function that relates them.
This activity is appropriate for an Algebra 1 classroom or review for an Algebra 2 class.
Students are to enter the data from the table on the worksheet into lists and
Be sure that students have cleared all lists before beginning. To do this, press STAT, then select ClrAllLists.
Students will then create a scatter plot of the data using Plot1.
They are to describe the relationship of and . As the values increase, the values decrease. The rate is not constant; the amount of change in decreases as increases.
For list , students will enter the formula multiplying the values by the values.
The formula might be used for the area of , where is the length and is the width.
When students solve the equation for , they should get and enter this in .
As students view the function table, they should see that the function is undefined at .
They should also see that the negative values have the same values, although negative, as the positive values.
When students view the entire graph, they should confirm that is undefined at zero (vertical and horizontal asymptotes at zero).
The graph does not appear in Quadrants II or IV because the and values have the same sign.
An inverse variation could be in Quadrants II or IV, if the coefficient is negative.