To find the average rate of change of a function \( f \) over the interval \([a, b] = [3, 4]\), we use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
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Identify the values of \( f(3) \) and \( f(4) \):
- From the graph, determine the corresponding \( y \)-values for \( x = 3 \) and \( x = 4 \) (these are generally provided by the graph, but since we don't have the image, I'll indicate that you should use the actual \( y \)-values from your graph).
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Substitute these values into the formula:
- Let’s say \( f(3) \) corresponds to some value \( y_3 \) and \( f(4) \) corresponds to \( y_4 \).
- Plug these into the average rate of change formula:
\[ \text{Average Rate of Change} = \frac{y_4 - y_3}{4 - 3} = y_4 - y_3 \]
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Calculate the result:
- Evaluate \( y_4 - y_3 \).
Once you have calculated the \( y \)-values from your curve at \( x = 3 \) and \( x = 4 \), perform the subtraction to determine the average rate of change.
Assuming you've gathered the correct values:
- If for example \( f(3) = 20 \) and \( f(4) = 4 \) (hypothetical values from your graph), the calculation would be:
\[ \text{Average Rate of Change} = 4 - 20 = -16 \]
Based on the hypothetical calculation, the average rate of change over the interval \([3, 4]\) would be \(-16\).
To finalize, please check the actual \( y \)-values from your graph for \( f(3) \) and \( f(4) \) and follow through with the calculation. But the typical answer choice would be marked as −16 if that corresponds with your graph values.
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