Compare two functions represented in different ways: equations, graphs, tables, or verbal descriptions.
Distinguish linear and exponential tables
Problem
Use the \(\text{two}\) displayed output tables for consecutive integer inputs. Classify each table as linear or exponential and give the constant-difference or constant-ratio evidence.
Increasing outputs alone do not identify a function family; the kind of repeated change does. Since the inputs advance by equal steps, we’ll test consecutive outputs in two ways: subtraction for a constant additive pattern and division for a constant multiplicative pattern. The test that stays constant supplies both the classification and its evidence.
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