Function Model Selection and Assumption Articulation

Choosing a function model is a claim about how a quantity changes. Linear claims equal change per step; quadratic claims the changes themselves change by a constant; rational claims two quantities trade off so their product holds still. The reliable evidence is the rate signature read from a difference table (with equally spaced inputs), never the silhouette of the graph, because over a short window a quadratic, an exponential, and a steep line all wear the same costume.

The mistakes here are shape-matching instead of rate-reading, difference tables run without checking the input spacing, and models trusted outside the window where their assumption was tested. The lesson drills all three, and adds the habit the CED asks for by name: stating what your model assumes, and where the context ends its domain.