Identifying the Average Rate of Change

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Presentation transcript:

Identifying the Average Rate of Change Adapted from Walch Education

Average of Rate 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. 5.5.3: Identifying the Average Rate of Change

Average Rate of 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. 5.5.3: Identifying the Average Rate of Change

Practice # 1 Calculate the average rate of change for the function f(x) = x2 + 6x + 9 between x = 1 and x = 3. 5.5.3: Identifying the Average Rate of Change

Evaluate the function for x = 3 and x = 1 f(x) = x2 + 6x + 9 Original function f(3) = (3)2 + 6(3) + 9 Substitute 3 for x. f(3) = 36 Simplify. f(x) = x2 + 6x + 9 Original function f(1) = (1)2 + 6(1) + 9 Substitute 1 for x. f(1) = 16 Simplify. 5.5.3: Identifying the Average Rate of Change

Use the average rate of change formula Substitute 1 for a and 3 for b. Substitute the values for f(3) and f(1). Simplify. 5.5.3: Identifying the Average Rate of Change

You Try. Use the graph of the function at right to calculate the average rate of change between x = –3 and x = –2. 5.5.3: Identifying the Average Rate of Change

Thanks for Watching! Ms. Dambreville