To find the average rate of change of a function \( f(x) \) over the interval \([1, 4]\), we use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
where \( a = 1 \) and \( b = 4 \).
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Identify the function values at the endpoints of the interval:
- \( f(1) \): Look at the graph and find the value of \( f(1) \) (let's assume it is 2, but this would depend on the graph).
- \( f(4) \): Look at the graph and find the value of \( f(4) \) (let's assume it is 5, but this would also depend on the graph).
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Plug those values into the formula:
\[ \text{Average Rate of Change} = \frac{f(4) - f(1)}{4 - 1} \]
Assuming \( f(1) = 2 \) and \( f(4) = 5 \):
\[ \text{Average Rate of Change} = \frac{5 - 2}{4 - 1} = \frac{3}{3} = 1 \]
If the values of \( f(1) \) and \( f(4) \) differ based on the actual graph, make sure to replace them accordingly.
From the options provided:
- The average rate of change is 1.
So, if \( f(1) \) and \( f(4) \) are as assumed here, the average rate of change is indeed 1. If the values were different, you'd recalculate but stick with the logic above.
Please choose the option: The average rate of change is 1.