Question

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

Answer 1

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

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

In this case, we need the values of the function at \(x = 3\) and \(x = 4\) from the graph.

Let's denote:
- \(f(3)\) as the function value at \(x = 3\)
- \(f(4)\) as the function value at \(x = 4\)

Assuming you can read these values from the graph (let’s just say we found that \(f(3) = y_3\) and \(f(4) = y_4\)), plug these values into the formula.

1. Calculate \(f(4) - f(3)\).
2. Divide the result by \(4 - 3\) (which is 1).

So the average rate of change simplifies to:

\[
f(4) - f(3)
\]

Once you determine \(f(3)\) and \(f(4)\):

- If, for example, \(f(3) = 0\) and \(f(4) = -16\), then:

\[
\text{Average Rate of Change} = -16 - 0 = -16
\]

If you provide the specific function values from the graph at \(x = 3\) and \(x = 4\), I could help you calculate the exact average rate of change. If you have access to those values, please share!