At the end of this lesson, students will be able to:
- Identify functions using differences and ratios.
- Write equations for functions.
- Perform exponential and quadratic regressions with a graphing calculator.
- Solve real-world problems by comparing function model.
Terms introduced in this lesson:
ratio of the differences
constant ratio of differences
exponential, quadratic regression
Teaching Strategies and Tips
Emphasize that students should always begin a regression by drawing the scatter plot of the data. This allows them to determine which function of best fit is most appropriate, if any.
- A regression is a curve that comes as close as possible to all the data points without being another type of function.
- Regressions do not necessarily pass through data points. Therefore, y−values will be different from those in the data set.
Remind students to check in general the differences in x−values that they are constant.
In Review Questions 4-6 and 12, remind students to calculate the differences of the differences to see if a quadratic trend exists. Students often calculate only the first set of differences.