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Use the image to answer the question.

A coordinate plane shows a curve labeled f of x. The x-axis ranges from negative 1 to 5 in 1-unit increments. The y-axis ranges from negative 2 to 30 in increments of 2. 2 points are marked on the curve.

Calculate the average rate of change over the interval [3,4]
of the given graph of the function.

(1 point)
Responses

16
16

8
8

−16
negative 16

116

1 answer

To calculate the average rate of change of a function \( f(x) \) 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, you're asked to find the average rate of change over the interval \([3, 4]\).

You'll need the values of \( f(3) \) and \( f(4) \) from the graph.

  1. Find the value of \( f(3) \) at \( x = 3 \).
  2. Find the value of \( f(4) \) at \( x = 4 \).
  3. Plug these values into the average rate of change formula.

Since I don't have the image or values from the curve, I can't compute the exact average rate of change. Please provide the specific \( y \)-values for \( f(3) \) and \( f(4) \) so I can help you finish the calculation!

For your options, ensure you have the correct values, and then perform the calculation.