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. Consider the graph of f (x) = J} given below. a)What is f(1)? b)What is f(9)? c) The points A[l, _] and B[9, _] lie on the curve. Label the points on the graph above. d] If we draw a line connecting these two points. we have a secant line to the curve. What is the slope of this secant line joining A and B? e) What is another name for the slope of the secant line joining A and B? 3. In the graph below, a secant line intersects the graph of y = f (x) at two points. Label the points P and Q. Suppose that the x-coordinate of point P is a, and the x-coordinate of point Q is b. a] Represent the coordinates of P and Q _ b] Represent the slope of the line joining P and Q using the coordinates. c] True or False? The slope of the secant line is the average rate of change of the function between the two points. 4. Suppose you run for exercise at different rates. Suppose the curve defined by the function d(t) = t2 + 1 models the distance you have run in meters at t seconds. What is your instantaneous rate of change at 4 seconds into the run? Procedure: A. Evaluate the function at each time listed below and fill in the following table. Note that the times are close to t = 4 from both sides. Use a calculator. A B C D E t = 3.9 t = 3.99 t = 4 t = 4.01 t = 4.1 d(3.9) = d(3.99) = d(t) = d(4.01) = d(4.1) = B. Now calculate the slope for each of the four secant lines. Use a calculator. Slope between Slope between Slope at C Slope between Slope between A and C B and C C and D C and E Estimate: m = m = m = m = C. Finally, looking at the slopes of the secant lines approaching Point C from both sides, estimate the instantaneous rate of change at t = 4 seconds:MATH 2211 PRACTIS WORKSHEET [2 .1) Calculus Topic: Using average rate of change to approximate instantaneous rate of change Precalculus Topic: Evaluating a function and using the slope formula Name 1. Given the points A(2, 8) and 3(4, 3) a] Find the change in y-values, yz yl b] Find the change in x-values, x2 x1 c} Find the slope of the line joining the two points. d] The slope is negative. What does this indicate about the line