To calculate the average rate of change of a function \( f(x) \) over an interval \([a, b]\), we use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In your case, the interval is \([3, 4]\). This means \( a = 3 \) and \( b = 4 \).
To find \( f(3) \) and \( f(4) \), you would typically look up these values from the graph of the function. Once you have these values, you can substitute them into the formula.
Assuming you found (for example):
- \( f(3) = y_1 \)
- \( f(4) = y_2 \)
Next, substitute these values into the formula:
\[ \text{Average Rate of Change} = \frac{y_2 - y_1}{4 - 3} = y_2 - y_1 \]
After performing the calculation, you'd get the average rate of change over the interval \([3, 4]\).
To provide an exact answer, please specify the values of \( f(3) \) and \( f(4) \) from the graph. If these values correspond to specific choices, I can help you determine the correct option from the answers provided.
1 answer