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Calculating & Interpreting the Average Rate of Change of Polynomials The Average rate of change of a function y f ( x) over an interval [a,b] is: y f (b) f (a ) x ba 1) Find the average rate of change of the linear function f ( x) 3x 4 for the interval [-2,1]. y _________ x 2) Using the table, Find the average rate of change of the linear function for the interval [-2,-1] and [0,2]. Is the average rate of change the same? x -2 -1 0 2 y 2 -1 -4 -10 3) The table below shows the elapsed time when two different cars pass a 10,20,30,40 and 50 meter on a test track. a) For car 1, what is the average velocity between the 0 and 10 meter mark? Between the 0 and 50 mark? Between the 20 and 30 meter mark? Analyze the data to describe the motion of the car 1. b) How does the velocity of car 1 compare to that of car 2? d 10 20 30 40 50 Car 1 t 4.472 6.325 7.746 8.944 10 Car 2 t 1.742 2.899 3.831 4.633 5.348 Calculating & Interpreting the Average Rate of Change of Polynomials 4) Find the average rate of change of f ( x) ( x 3)2 a) Interval [1,3] _______ b) Interval [4,7]. _______ c) Compare & contrast the two average rates of change. 5) The value of an antique has increased exponentially, as shown in this graph. Based on the graph, estimate to the nearest $50 the average rate of change for the following time intervals. From 0 to 20 years: _________ From 20 to 40 years: _________ Calculating & Interpreting the Average Rate of Change of Polynomials 6) Find the average rate of change of the following the function over intervals: a) [-2,-1] b) 2 x 1 c) From x 2 to x 1 d) Compare and contrast these intervals. 7) Find the average rate of change of the following intervals from the graph above. a) [-2,-1] b) [-1, 2] c) [2, 3] d) Compare and contrast these intervals.