Average Rate of Change
The average rate of change refers to the average rate at which one quantity changes in relation to another over a specific interval
The average rate of change refers to the average rate at which one quantity changes in relation to another over a specific interval. It measures how much a quantity on the y-axis changes on average for each unit of change on the x-axis.
To calculate the average rate of change, we need to determine the difference in the y-values (change in the dependent variable) divided by the difference in the x-values (change in the independent variable) over a given interval.
The formula for calculating the average rate of change is:
Average Rate of Change = (change in y) / (change in x)
For example, let’s say we have a linear function f(x) = 3x + 2. If we want to calculate the average rate of change of this function between x = 2 and x = 5, we can substitute these values into the function to find the corresponding y-values:
f(2) = 3(2) + 2 = 8
f(5) = 3(5) + 2 = 17
The change in y (Δy) between these two points is 17 – 8 = 9, and the change in x (Δx) is 5 – 2 = 3. Therefore, the average rate of change is:
Average Rate of Change = (9) / (3) = 3
This means that, on average, for each unit of increase in x, the value of y increases by 3.
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