Inverse Function

By Matthew Estes •

Grade Level	12th
Subject Area	Math
Duration	Two 70 minute class periods
Setting	Regular Classroom
Background Knowledge	The students should be able to: Solve simple algebraic equations. Find a regression line using their calculators.
Author	Matthew Estes

Summary
This activity will allow the students to record their own data periodically, in this case temperatures using some Texas Instruments external calculator hardware. They will then derive an equation relating time of year to ocean temperature. They will also use a function for the chance of a hurricane based on the ocean’s temperature to explain the frequency of hurricanes during a particular season. By finding the inverse of the two functions, the one they found as well as the one they were given, they will be able to convert between three different data sets.

Objectives
Students will be able to: 1. Calculate an inverse function. 2. Understand the practicality of inverse functions in the real world.

Materials
One mug. One shallow bowl. One Microwave. One faucet. One external TI temperature sensor. One calculator per student. One handout per student

Ohio Standards
Benchmark: Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators. Indicators: Create a scatterplot of bivariate data, identify trends, and find a function to model the data. Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation. Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. Benchmark: Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior. Indicator: Represent the inverse of a function symbolically and graphically as a reflection about y = x.