Identifying the Average Rate of Change

Adapted from Walch EducationIdentifying the Average Rate of Change

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. 25.5.3: Identifying the Average Rate of ChangeAverage of Rate Change

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.

35.5.3: Identifying the Average Rate of ChangeAverage Rate of Change

Calculate the average rate of change for the function f(x) = x2 + 6x + 9 between x = 1 and x = 3.45.5.3: Identifying the Average Rate of ChangePractice # 155.5.3: Identifying the Average Rate of ChangeEvaluate the function for x = 3 and x = 1f(x) = x2 + 6x + 9Original functionf(3) = (3)2 + 6(3) + 9 Substitute 3 for x. f(3) = 36 Simplify. f(x) = x2 + 6x + 9Original functionf(1) = (1)2 + 6(1) + 9 Substitute 1 for x. f(1) = 16Simplify. 65.5.3: Identifying the Average Rate of ChangeUse the average rate of change formula

Average rate of change formulaSubstitute 1 for a and 3 for b.Simplify.

Substitute the values for f(3) and f(1). Use the graph of the function at right to calculate the average rate of change between x = 3 and x = 2.75.5.3: Identifying the Average Rate of ChangeYou Try.

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