The foundation of the whole course. How output values change in tandem with input, average and instantaneous rates of change, concavity, polynomial zeros and end behavior, and everything that makes rational functions behave the way they do — asymptotes, holes, and all.
Six ways to master Unit 1 — pick whichever fits how you like to study.
All 14 topics from the College Board CED, in order.
Unit 1 is where AP Precalculus establishes its central idea: a function describes two quantities changing in tandem. You'll learn to describe that change precisely — where a function increases or decreases, whether it's concave up or concave down, and how fast it's changing both on average over an interval and at a single point.
From there the unit dives into the two headline function families. Polynomial functions are studied through their zeros (real and complex, with multiplicity) and their end behavior, which is set entirely by the leading term. Rational functions add the ideas that give them their distinctive graphs — vertical asymptotes, horizontal and slant asymptotes, and holes — all of which come from comparing the numerator and denominator.
This unit is the largest on the exam at 30–40% and takes about 30–40 class periods. Because rates of change, transformations, and modeling all reappear in Units 2 and 3, mastering Unit 1 pays off across the entire course. The three mathematical practices below are woven through every topic: