Comparing functions
Linear has constant first differences, quadratic constant second differences, exponential constant ratios. Students classify tables, graphs, and stories, compare growth over an interval, and explain why exponential growth eventually wins.
Specification · for a parent or teacher
- comparing-function-families
- High School Math 1 · Unit 12
- Change
- 4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
- 5 items
Students can
classify a table, graph, or story as linear, quadratic, or exponential from differences and ratios; compare growth rates over an interval; explain why exponential growth eventually exceeds polynomial growth.
Ready when
three tables, three identifications, and a sentence about why exponential wins for large .
Watch for
a table with almost constant first differences called linear; of a scatter plot used here (that is ch. 18).