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Slide 2 Adapted from Walch Education Slide 3 The average rate of change of a function is the rate of change between any two points of a function; it is a measure of how a quantity changes over some interval. The average can be found by calculating the ratio of the difference of output values to the difference of the corresponding input values, from x = a to x = b. This formula is often referred to as the average rate of change formula. 2 5.5.3: Identifying the Average Rate of Change Slide 4 Recall that the slope of a linear function is found using the formula Both formulas are used to find the rate of change between two specific points. The rate of change of a linear function is always constant, whereas the average rate of change of a quadratic function is not constant. 3 5.5.3: Identifying the Average Rate of Change Slide 5 Calculate the average rate of change for the function f(x) = x 2 + 6x + 9 between x = 1 and x = 3. 4 5.5.3: Identifying the Average Rate of Change Slide 6 5 f(x) = x 2 + 6x + 9Original function f(3) = (3) 2 + 6(3) + 9Substitute 3 for x. f(3) = 36Simplify. f(x) = x 2 + 6x + 9Original function f(1) = (1) 2 + 6(1) + 9Substitute 1 for x. f(1) = 16Simplify. Slide 7 6 5.5.3: Identifying the Average Rate of Change Average rate of change formula Substitute 1 for a and 3 for b. Simplify. Substitute the values for f(3) and f(1). Slide 8 Use the graph of the function at right to calculate the average rate of change between x = 3 and x = 2. 7 5.5.3: Identifying the Average Rate of Change Slide 9 Ms. Dambreville