Question
What is the average rate of change of a function on the interval x:[4,8]
𝑥
:
[
4
,
8
]
?
(12.5, 7)
(1 point)
Responses
4
4
12
12
11
11
3
𝑥
:
[
4
,
8
]
?
(12.5, 7)
(1 point)
Responses
4
4
12
12
11
11
3
Answers
GPT-4o mini
The average rate of change of a function \( f(x) \) on the interval \( [a, b] \) is given by the formula:
\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]
In this case, you are given two points: \( (4, 12.5) \) and \( (8, 7) \). Here, \( a = 4 \) and \( b = 8 \).
Using the values:
- \( f(4) = 12.5 \)
- \( f(8) = 7 \)
Now, plug these values into the formula:
\[
\text{Average rate of change} = \frac{7 - 12.5}{8 - 4}
\]
Calculate the numerator and the denominator:
\[
\text{Average rate of change} = \frac{-5.5}{4} = -1.375
\]
Since none of the provided options (4, 12, 11, 3) relate to this calculation, it appears that the function \( f(x) \) needs further context or a different interpretation for those specific options. However, based on the points given, the average rate of change is \( -1.375 \).
\[
\text{Average rate of change} = \frac{f(b) - f(a)}{b - a}
\]
In this case, you are given two points: \( (4, 12.5) \) and \( (8, 7) \). Here, \( a = 4 \) and \( b = 8 \).
Using the values:
- \( f(4) = 12.5 \)
- \( f(8) = 7 \)
Now, plug these values into the formula:
\[
\text{Average rate of change} = \frac{7 - 12.5}{8 - 4}
\]
Calculate the numerator and the denominator:
\[
\text{Average rate of change} = \frac{-5.5}{4} = -1.375
\]
Since none of the provided options (4, 12, 11, 3) relate to this calculation, it appears that the function \( f(x) \) needs further context or a different interpretation for those specific options. However, based on the points given, the average rate of change is \( -1.375 \).