Use the image to answer the question. Calculate the average rate of change over the interval [−1,1] using the given graph of the function. (1 point) The average rate of change is .

Question

-1,-9 1,3

Answer 1

To calculate the average rate of change of a function over an interval \([a, b]\), you can use the formula:

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

In this case, the interval is \([-1, 1]\):

• At \(x = -1\), the function value \(f(-1) = -9\).
• At \(x = 1\), the function value \(f(1) = 3\).

Now, plug these values into the formula:

\[ \text{Average Rate of Change} = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{3 - (-9)}{1 + 1} = \frac{3 + 9}{2} = \frac{12}{2} = 6 \]

Thus, the average rate of change over the interval \([-1, 1]\) is 6.