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. the 2 points are: 3,4 and 4,20.

Calculate the average rate of change over the interval [3,4] of the given graph of the function.

(1 point)
Responses

16
16

−16
negative 16

116
Start Fraction 1 over 16 End Fraction

8
8

Answer 1

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

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

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

From the points given:

• \( f(3) = 4 \)
• \( f(4) = 20 \)

Now, substitute these values into the formula:

\[ \text{Average Rate of Change} = \frac{f(4) - f(3)}{4 - 3} = \frac{20 - 4}{4 - 3} = \frac{16}{1} = 16 \]

Therefore, the average rate of change over the interval \([3, 4]\) is \( 16 \).

The correct response is:

16