Use the image to answer the question.

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

116
Start Fraction 1 over 16 End Fraction

16
16

8
8

−16

Answer 1

To calculate the average rate of change of the function \( f(x) \) over the interval \([3, 4]\), we use the formula:

\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]

where \( a = 3 \) and \( b = 4 \).

You need the values of \( f(3) \) and \( f(4) \) from the graph. Assuming you have the data points from the graph:

1. Determine \( f(3) \) and \( f(4) \) from the graph (let's say, for example, \( f(3) = 16 \) and \( f(4) = 32 \)).

2. Plug the values into the formula:

\[ \text{Average Rate of Change} = \frac{f(4) - f(3)}{4 - 3} = \frac{32 - 16}{1} = \frac{16}{1} = 16 \]

Choosing the closest matching option based on our example, the answer would be \( 16 \).

However, please ensure you check the actual graph for precise points to plug into the formula for accurate calculation. If \( f(3) \) and \( f(4) \) yield different specific values, substitute those in the average rate of change formula for your answer.