Question

Average Rate of Change Quick Check
2 of 52 of 5 Items

Question
Use the image to answer the 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

16
16

8
8

−16
negative 16

116
Start Fraction 1 over 16 End Fraction
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Answer 1

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

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

In your case, the interval is \([3, 4]\). You'll need the values of \( f(3) \) and \( f(4) \) from the graph.

1. Identify the coordinates at \( x = 3 \) and \( x = 4 \) on the graph. Let's assume for illustration that:
- \( f(3) = y_1 \) (the y-value at \( x = 3 \))
- \( f(4) = y_2 \) (the y-value at \( x = 4 \))

2. Plug these values into the average rate of change formula:

\[
\text{Average Rate of Change} = \frac{y_2 - y_1}{4 - 3} = y_2 - y_1
\]

3. After calculating, you'll arrive at one of the responses you provided (16, 8, -16, or \(\frac{1}{16}\)).

Since I don't have a visual of the graph right now, please refer to the graph to find the specific values for \( f(3) \) and \( f(4) \) that you can substitute into the formula. Then you'll be able to choose the correct response.