In two or more complete sentences, explain how to find the average rate of change of a function.
Question
In two or more complete sentences, explain how to find the average rate of change of a function.
Solution
To find the average rate of change of a function, you need to follow these steps:
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Choose two points on the function: Select two distinct values of the independent variable, such as x1 and x2.
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Calculate the corresponding function values: Plug the chosen values of x into the function to find the corresponding y values, denoted as f(x1) and f(x2).
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Determine the change in y: Subtract the initial function value from the final function value to find the difference in y, which is f(x2) - f(x1).
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Calculate the change in x: Subtract the initial x value from the final x value to find the difference in x, which is x2 - x1.
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Find the average rate of change: Divide the change in y by the change in x, which is (f(x2) - f(x1)) / (x2 - x1).
The resulting value represents the average rate of change of the function between the two chosen points.
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