AP Precalculus – Polynomial Functions and Rates of Change – Drill 3

About This Drill

AP Precalculus – Polynomial Functions and Rates of Change – Drill 3 is a Math practice drill covering Polynomial Functions and Rates of Change. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice reading local extrema, inflection points, and rates of change from polynomial graphs and models. This AP® Precalculus drill covers Topic 1.4 skills tested on the AP® exam, including identifying where a polynomial function is increasing at an increasing or decreasing rate.

Questions in This Drill

1. 
   
   The graph of a polynomial function f is shown above for x on the interval [0, 5]. On which of the following intervals is f both increasing and concave up?
2. The table below shows selected values of a polynomial function h.
   
   

   x	0	1	2	3	4
   h(x)	2	5	10	17	26

   
   Which of the following best describes the behavior of h on the interval [0, 4]?
3. The rate at which water flows into a reservoir is modeled by the function r(t) = −t² + 4t + 5, where r is measured in thousands of gallons per hour and t is measured in hours, for 0 ≤ t ≤ 5. At what value of t does the flow rate change from increasing to decreasing?
4. 
   
   The graph of a polynomial function f is shown above for x on the interval [0, 5]. Which of the following correctly identifies a local extremum of f and describes the behavior of f at that point?
5. The function f is a polynomial with f(1) = 0 and f(3) = 4. The average rate of change of f on [1, 3] is 2. A student claims that f must be increasing at a constant rate on [1, 3]. Which of the following, if true, would prove the student's claim is incorrect?