AP Precalculus Rate of Change & Concavity Sign Charts: Table & Graph FRQ Checklist
Across AP Precalculus Unit 1 (Polynomial and Rational Functions), the single highest-frequency exam trap confuses whether a function is increasing with whether its rate of change is increasing.
Key Exam Takeaway: To earn full justification credit on AP Precalculus FRQs, always compute consecutive average rates of change from the table and explicitly state whether those rates of change are increasing (concave up) or decreasing (concave down) on the open interval.
Step-by-Step Scoring & Classroom Checklist
- Increasing vs. Decreasing: f is increasing on an interval when inputs x2 > x1 yield outputs f(x2) > f(x1) (positive average rate of change).
- Concave Up vs. Concave Down: A graph is concave up when the average rate of change is increasing across consecutive intervals, even if the function itself is currently decreasing.
- Points of Inflection: Occur only where concavity switches sign (from concave up to concave down, or vice versa).
- Worked Video & Printable Table Sets: Watch sequential AP Precalculus lessons on @BenchmarkAP (https://www.youtube.com/@BenchmarkAP) and grab printable guided notes at https://www.teacherspayteachers.com/store/benchmark-ap.