Question

What is the average rate of change of the function graphed on the interval x:[1,3] ?

image shows (1, -1) going all the way up to (3, 25)

Answer 1

The average rate of change of a function on a given interval \([a, b]\) can be calculated using the formula:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

In your case, the function changes from the point \((1, -1)\) to the point \((3, 25)\).

Here, we have:
- \(a = 1\)
- \(b = 3\)
- \(f(a) = f(1) = -1\)
- \(f(b) = f(3) = 25\)

Now, substituting these values into the formula:

\[
\text{Average Rate of Change} = \frac{25 - (-1)}{3 - 1} = \frac{25 + 1}{2} = \frac{26}{2} = 13
\]

Thus, the average rate of change of the function on the interval \([1, 3]\) is \(13\).