Understanding Average Rate of Change in Math: Definition and Examples

average rate of change

f(b)-f(a)/b-a

The average rate of change refers to the slope of a line that connects two points on a graph of a function over a certain interval. It is calculated by finding the difference in the function’s values at the endpoints of the interval, and then dividing the difference by the length of the interval.

More specifically, if we have a function f(x), and we want to find the average rate of change between two points x1 and x2, we use the following formula:

average rate of change = (f(x2) – f(x1))/(x2 – x1)

This formula tells us how much the function changes on average for each unit change in x between x1 and x2.

For example, let’s say we have the function f(x) = 2x + 1, and we want to find the average rate of change between x = 1 and x = 3. Using the formula above, we get:

average rate of change = (f(3) – f(1))/(3 – 1) = (2(3) + 1) – (2(1) + 1))/2 = 4

This means that on average, for each unit increase in x between x = 1 and x = 3, the function f(x) increases by 4.

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