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

8
8

116
Start Fraction 1 over 16 End Fraction

16
16

−16
negative 16
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Answer 1

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

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

In this case, we are calculating the average rate of change over the interval \([3, 4]\).

You will need to find the values of the function \( f(3) \) and \( f(4) \) from the graph.

1. Identify the value of \( f(3) \) where \( x = 3 \).
2. Identify the value of \( f(4) \) where \( x = 4 \).
3. Plug these values into the formula.

Suppose \( f(3) = a \) and \( f(4) = b \), then:

\[ \text{Average Rate of Change} = \frac{b - a}{4 - 3} = b - a \]

Without the image to see the specific values of \( f(3) \) and \( f(4) \), I cannot provide a numerical answer. However, once you obtain \( f(3) \) and \( f(4) \) from the graph, substitute those values into the equation to find the average rate of change.

You can then match your result with the multiple-choice answers provided.