Selected values of a function f are shown in the table above. What is the average rate of change of f over the interval [1,5] ?
To find the average rate of change of a function over an interval, we need to calculate the difference in the function’s values divided by the difference in the independent variable values
To find the average rate of change of a function over an interval, we need to calculate the difference in the function’s values divided by the difference in the independent variable values.
In this case, let’s consider the function f represented by the table:
| x | f(x) |
|—-|——|
| 1 | 3 |
| 3 | 7 |
| 5 | 9 |
The interval we are interested in is [1, 5], which means we need to find the average rate of change of f between x = 1 and x = 5.
To calculate the average rate of change, we start by finding the change in f(x) over the interval. This can be done by subtracting the initial value of f from the final value of f:
Change in f(x) = f(5) – f(1) = 9 – 3 = 6.
Next, we find the change in x over the interval by subtracting the initial value of x from the final value of x:
Change in x = 5 – 1 = 4.
Finally, we divide the change in f(x) by the change in x to find the average rate of change:
Average rate of change = (Change in f(x)) / (Change in x) = 6 / 4 = 1.5.
Therefore, the average rate of change of f over the interval [1, 5] is 1.5.
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