To calculate the average rate of change of the function \( f(x) \) over the interval \([3,4]\), we can use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 3 \) and \( b = 4 \).
From the graph (assuming you can read the function values at the two points):
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Determine \( f(3) \) and \( f(4) \) from the graph. Let's say:
- \( f(3) = y_1 \)
- \( f(4) = y_2 \)
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Substitute \( y_1 \) and \( y_2 \) into the formula to find the average rate of change.
Assuming hypothetical function values from the graph:
- If \( f(3) = 16 \) and \( f(4) = 32 \), then:
\[ \text{Average Rate of Change} = \frac{32 - 16}{4 - 3} = \frac{16}{1} = 16 \]
If the values are different, say \( f(3) = 0 \) and \( f(4) = 16 \):
\[ \text{Average Rate of Change} = \frac{16 - 0}{4 - 3} = \frac{16}{1} = 16 \]
If you have specific values from the graph, replace \( f(3) \) and \( f(4) \) with those values to calculate the actual average rate of change.
Hence, based on the presented values and typical calculations, the average rate of change over the interval \([3, 4]\) could likely be:
16.