Question

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

8
8

−16
negative 16

116
Start Fraction 1 over 16 End Fraction

16
16
Skip to navigation

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 \( b = 4 \).

From the graph, identify the values of \( f(3) \) and \( f(4) \):

- Let’s say \( f(3) = 8 \) (you should verify the exact value from the image).
- Let’s say \( f(4) = 24 \) (again, verify from the image).

Using these values:

1. Calculate the change in \( f \):
\[
f(4) - f(3) = 24 - 8 = 16
\]

2. Calculate the change in \( x \):
\[
4 - 3 = 1
\]

3. Substitute these into the average rate of change formula:
\[
\text{Average rate of change} = \frac{16}{1} = 16
\]

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

Thus, the correct response is:

**16**