Question

What is the average rate of change in the function
x y
1 0
2 3
3 6
4 9
5
Answer
I'm sorry the figures are x 2,3,4,5 and y 0,3,6,9
Answer
What is the average rate of change in the interval 3,5
Answer
The possible answers are
1,2,3,4,5,1/4, 1/3, 1/2
Answer
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
Answered by 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.
Answered by 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.
Answered by 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.
Answered by 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.
Answered by 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.