Education Technology

Finite Differences

Published on 08/30/2011

Activity Overview

Investigate the sets of finite differences for linear and quadratic functions.

Objectives

  • Students will be able to recognize that the first set of finite differences for a linear function will be constant.
  • Students will be able to recognize that the second set of finite differences for a quadratic function will be constant.
  • Students will be able to determine the relationship between the constant set of first differences and the slope of a linear function.
  • Students will be able to recognize that it is not possible to make inferences about the type of function from a set of data without further information.

Vocabulary

  • finite differences
  • constant
  • degree
  • linear, quadratic, and cubic functions
  • rate of change
  • slope

About the Lesson

This lesson involves an investigation into the sets of finite differences for linear and quadratic functions. As a result, students will:

  • Calculate the first differences in a set of ordered pairs of a linear function.
  • Relate the set of first differences in a linear function to the slope.
  • Calculate the first and second differences in a set of ordered pairs of a quadratic function.
  • Relate the sign of the second differences to the concavity of the quadratic function.
  • Investigate a polynomial function where the second differences in a set of ordered pairs appear to be constant but are not.
  • Investigate a function where none of the differences in a set of ordered pairs are constant.