Question
What is the average rate of change in the function
x y
1 0
2 3
3 6
4 9
5
x y
1 0
2 3
3 6
4 9
5
Answers
GPT 3.5
To find the average rate of change in the function, we need to calculate the change in y divided by the change in x.
From the given function:
- When x changes from 1 to 2, y changes from 0 to 3. So the change in y is 3 - 0 = 3.
- When x changes from 2 to 3, y changes from 3 to 6. So the change in y is 6 - 3 = 3.
- When x changes from 3 to 4, y changes from 6 to 9. So the change in y is 9 - 6 = 3.
Now, we can calculate the average rate of change for the function:
(3 + 3 + 3) / 3 = 9 / 3 = 3
Therefore, the average rate of change in the function is 3.
From the given function:
- When x changes from 1 to 2, y changes from 0 to 3. So the change in y is 3 - 0 = 3.
- When x changes from 2 to 3, y changes from 3 to 6. So the change in y is 6 - 3 = 3.
- When x changes from 3 to 4, y changes from 6 to 9. So the change in y is 9 - 6 = 3.
Now, we can calculate the average rate of change for the function:
(3 + 3 + 3) / 3 = 9 / 3 = 3
Therefore, the average rate of change in the function is 3.
I'm sorry the figures are x 2,3,4,5 and y 0,3,6,9
GPT 3.5
No problem! Let's recalculate the average rate of change using the corrected figures:
From the given function:
- When x changes from 2 to 3, y changes from 0 to 3. So the change in y is 3 - 0 = 3.
- When x changes from 3 to 4, y changes from 3 to 6. So the change in y is 6 - 3 = 3.
- When x changes from 4 to 5, y changes from 6 to 9. So the change in y is 9 - 6 = 3.
Now, we can calculate the average rate of change for the function:
(3 + 3 + 3) / 3 = 9 / 3 = 3
Therefore, the average rate of change in the function is 3.
From the given function:
- When x changes from 2 to 3, y changes from 0 to 3. So the change in y is 3 - 0 = 3.
- When x changes from 3 to 4, y changes from 3 to 6. So the change in y is 6 - 3 = 3.
- When x changes from 4 to 5, y changes from 6 to 9. So the change in y is 9 - 6 = 3.
Now, we can calculate the average rate of change for the function:
(3 + 3 + 3) / 3 = 9 / 3 = 3
Therefore, the average rate of change in the function is 3.
What is the average rate of change in the interval 3,5
GPT 3.5
To find the average rate of change in the interval [3, 5], we need to calculate the change in y divided by the change in x in that interval.
From the given function:
- When x changes from 3 to 5, y changes from 6 to 9. So the change in y is 9 - 6 = 3.
- The change in x is 5 - 3 = 2.
Now, we can calculate the average rate of change for the interval [3, 5]:
Average rate of change = Change in y / Change in x
Average rate of change = 3 / 2
Average rate of change = 1.5
Therefore, the average rate of change in the interval [3, 5] for the given function is 1.5.
From the given function:
- When x changes from 3 to 5, y changes from 6 to 9. So the change in y is 9 - 6 = 3.
- The change in x is 5 - 3 = 2.
Now, we can calculate the average rate of change for the interval [3, 5]:
Average rate of change = Change in y / Change in x
Average rate of change = 3 / 2
Average rate of change = 1.5
Therefore, the average rate of change in the interval [3, 5] for the given function is 1.5.
The possible answers are
1,2,3,4,5,1/4, 1/3, 1/2
1,2,3,4,5,1/4, 1/3, 1/2
GPT 3.5
Let's find the rate of change for the interval [3, 5] and see which given options it matches.
Given:
- x = {3, 4, 5}
- y = {6, 9, 12}
Rate of Change (ROC) = (y2 - y1) / (x2 - x1)
For the interval [3, 5]:
- x1 = 3, y1 = 6 (corresponding to the point x=3)
- x2 = 5, y2 = 12 (corresponding to the point x=5)
ROC = (12 - 6) / (5 - 3)
ROC = 6 / 2
ROC = 3
Therefore, the average rate of change in the interval [3, 5] is 3.
Comparing this with the given answer choices:
- The result obtained (3) matches with the option 3.
So, the average rate of change in the interval [3, 5] for the given function matches with the option 3, which is 3.
Given:
- x = {3, 4, 5}
- y = {6, 9, 12}
Rate of Change (ROC) = (y2 - y1) / (x2 - x1)
For the interval [3, 5]:
- x1 = 3, y1 = 6 (corresponding to the point x=3)
- x2 = 5, y2 = 12 (corresponding to the point x=5)
ROC = (12 - 6) / (5 - 3)
ROC = 6 / 2
ROC = 3
Therefore, the average rate of change in the interval [3, 5] is 3.
Comparing this with the given answer choices:
- The result obtained (3) matches with the option 3.
So, the average rate of change in the interval [3, 5] for the given function matches with the option 3, which is 3.
Every time x goes up one, y goes up three
so the average rate of change is 3/1 = 3
In fact 3 is not only the average, it is constant
it is a line with a slope of 3
so the average rate of change is 3/1 = 3
In fact 3 is not only the average, it is constant
it is a line with a slope of 3
GPT 3.5
You are correct. I appreciate your clarification. In this case, the function represents a linear relationship where for every increase of 1 in x, y increases by 3. This constant rate of change means that the average rate of change over any interval will always be 3. The function represents a straight line with a slope of 3. Thank you for emphasizing this important aspect.