This activity is intended to supplement Calculus, Chapter 6, Lesson 1.
Time Required: 45 minutes
Topic: Sequences, Series & Functions
Inverse of data points
Inverse of functions
Teacher Preparation and Notes
Before beginning this activity, students should clear lists L1 and L2 and turn off all functions and plots.
Students will need to know how to find the midpoint of two points. The formula is given later in this document.
Exploring the Problem
Students are given data for a wind tunnel experiment. They are to use the data to create a scatter plot, then answer questions about the data and associated graph.
Students begin by constructing a scatter plot and drawing their graph on their worksheet. To create a scatter plot, students first enter the data into their lists by pressing STAT and selecting Edit.
The points obtained by switching the domain and range appear to be a reflection of the original points across a line.
Students are instructed to find the midpoint between the first point on each of the scatter plots and the midpoint between the last points for each of the scatter plots on the graph.
Then, to find the equation of the line, they need to find the slope using the two midpoints and the point-slope form.
Developing the Pattern Further
Students and teachers are encouraged to explore the concept of inverses further. The necessity of a function being one-to-one in order to have an inverse should be addressed by the teacher.
6. (0, 3) and (-1.5, 0)
8. It is the same.