Average Rate Of Change

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Average rate of change is the change in the quantity of one variable divided by the change in the other variable. Any function has an output value for a given input value. To calculate the rate of change for the given values, the change in its corresponding values of the function is calculated and divided by the difference in the input values.

Example 1: Find the average rate of change in the values for the function, f(x) = 3x+ 6 from 5 to 1.
Given if a function f(x) = 3x + 6.
Now, average rate of change is to be calculated for values from 5 to 1.
So finding their corresponding function values, we get:
f(5) = (3 * 5) + 6 = 15 + 6 = 21 
f(1) = (3 * 1) + 6 = 3 + 6 = 9
Change in values between 5 to 1 is f(5) - f(1) = 21 - 9 =12
Average rate of change = 12/ (5-1) = 3

 
Example 2: Find the average rate of change in the values for the function, f(x) = 2x+ 4 from 3 to 2.
Given if a function f(x) = 2x + 4.
Now, average rate of change is to be calculated for values from 3 to 2.
So finding their corresponding function values, we get:
f(3) = (2 * 3) + 4 = 6 + 4 = 10  
Then, f(2) = (2 * 2) + 4 = 4 + 4 = 8
Change in values between 3 to 2 is f(3) - f(2) = 10 - 8 = 2
Average rate of change = 2/ (3-2) = 2

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