Question
one plotted point is 4, 5
Use the image to answer the question.
A coordinate graph is shown. The horizontal axis spans from 0 to 9 in increments of 1 and the vertical axis spans from 0 to 19 in increments of 1.
What is the average rate of change of a function on the interval x:[4,8]
?
(1 point)
Responses
3
3
12
12
11
11
4
Use the image to answer the question.
A coordinate graph is shown. The horizontal axis spans from 0 to 9 in increments of 1 and the vertical axis spans from 0 to 19 in increments of 1.
What is the average rate of change of a function on the interval x:[4,8]
?
(1 point)
Responses
3
3
12
12
11
11
4
Answers
GPT-4o mini
To find the average rate of change of a function on the interval \( x: [4, 8] \), you can use the formula:
\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = 4 \) and \( b = 8 \).
From your question, you provided one plotted point which is (4, 5). We need to find the value of the function \( f(8) \) at \( x = 8 \). Since you mentioned "the image" but did not provide it, I can't see the coordinates at \( x = 8 \).
However, assuming the function's value at \( x = 8 \) is known or provided, we can calculate based on that value.
If we assume, for example, that \( f(8) = 17 \) (which might be the plotted point you need to reference), then we can plug in the values:
- \( f(4) = 5 \)
- \( f(8) = 17 \)
Now substitute into the average rate of change formula:
\[
\text{Average rate of change} = \frac{17 - 5}{8 - 4} = \frac{12}{4} = 3
\]
So if \( f(8) \) is indeed 17, the average rate of change would be \( 3 \).
If you have the actual value of \( f(8) \) from the image, please provide it and we can compute the exact average rate of change accordingly. If \( f(8) \) is not given, you will need to gather that information to finalize the answer. Based on the options provided, if you assume \( f(8) \) gives you an average rate of change of \( 3 \), that’s your correct choice.
\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = 4 \) and \( b = 8 \).
From your question, you provided one plotted point which is (4, 5). We need to find the value of the function \( f(8) \) at \( x = 8 \). Since you mentioned "the image" but did not provide it, I can't see the coordinates at \( x = 8 \).
However, assuming the function's value at \( x = 8 \) is known or provided, we can calculate based on that value.
If we assume, for example, that \( f(8) = 17 \) (which might be the plotted point you need to reference), then we can plug in the values:
- \( f(4) = 5 \)
- \( f(8) = 17 \)
Now substitute into the average rate of change formula:
\[
\text{Average rate of change} = \frac{17 - 5}{8 - 4} = \frac{12}{4} = 3
\]
So if \( f(8) \) is indeed 17, the average rate of change would be \( 3 \).
If you have the actual value of \( f(8) \) from the image, please provide it and we can compute the exact average rate of change accordingly. If \( f(8) \) is not given, you will need to gather that information to finalize the answer. Based on the options provided, if you assume \( f(8) \) gives you an average rate of change of \( 3 \), that’s your correct choice.