Question Use the image to answer the question. Calculate the average rate of change over the interval [3,4] of the given graph of the function. (1 point) Responses −16 negative 16 8 8 116 Start Fraction 1 over 16 End Fraction 16

Question

3,4 is at the bottom 4,20 at the top

Answer 1

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

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

From your question, it appears we have the values at the points:

• \(f(3) = 4\) (you mentioned that for \(x=3\), the value is at the bottom)
• \(f(4) = 20\) (you mentioned that for \(x=4\), the value is at the top)

Now, applying these values to the formula:

\[ \text{Average rate of change} = \frac{f(4) - f(3)}{4 - 3} = \frac{20 - 4}{4 - 3} = \frac{16}{1} = 16 \]

Thus, the average rate of change over the interval \([3, 4]\) is 16.