Which Function Is It?

Tables

Example 2

Does the table below represent a linear or a quadratic function?

FunctionTableEx2-1

Step 1. Find the first difference.


FunctionTableEx2-2

Step 2. If the first difference is constant, the function is linear. If not, find the second difference.

Since the first difference is not constant, find the second difference.

FunctionTableEx2-3

Step 3. If the second difference is constant, the function is quadratic. If not, label the function as other.

This table has a common second difference, so it is quadratic.
The function that models this table is FunctionTableEx2-4 .