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
*Note: This activity contains an optional AP Practice Questions document for those students preparing for the AP Precalculus Exam.