Average Rate of Change
The average rate of change is a concept in mathematics that measures the rate at which a quantity changes over a specific interval
The average rate of change is a concept in mathematics that measures the rate at which a quantity changes over a specific interval. It is often used to analyze and understand the behavior of functions and their graphs.
To calculate the average rate of change, you need to determine the change in the quantity (y-values) over the given interval (x-values). The formula for average rate of change (ARC) is:
ARC = (change in y) / (change in x)
Let’s understand this with an example:
Suppose we have a function f(x) = 2x + 3, and we want to find the average rate of change of the function between the x-values 2 and 5.
Step 1: Find the change in y
Evaluate the function f(x) at the two x-values:
f(2) = 2(2) + 3 = 7
f(5) = 2(5) + 3 = 13
The change in y is:
13 – 7 = 6
Step 2: Find the change in x
The change in x is the difference between the two x-values:
5 – 2 = 3
Step 3: Calculate the average rate of change
Plug the values from Step 1 and Step 2 into the formula:
ARC = (6) / (3) = 2
Therefore, the average rate of change of the function f(x) = 2x + 3 between x = 2 and x = 5 is 2.
This means that, on average, for every unit increase in x between 2 and 5, the function value increases by 2 units. It gives an overall measure of the slope or steepness of the function over that interval.
The average rate of change can also be negative if the function is decreasing over the given interval.
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