Question

What is the average rate of change CAN SOMEONE PLEASE ANSWER THIS QUESTION I WILL BRAINLIEST

Answer 1

Answer: The average rate of change for both is -2

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Explanation:

The x interval [0,3] is the same as writing $0 \le x \le 3$

It starts at x = 0 and ends at x = 3.

The graph shows that x = 0 leads to y = 3. So we have the point (0,3) on the parabola. We also have the point (3,-3) on the parabola.

Let's find the slope of the line through these endpoints.

$(x_1,y_1) = (0,3) \text{ and } (x_2,y_2) = (3,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - 3}{3 - 0}\\\\m = \frac{-6}{3}\\\\m = -2$

The slope is -2. This is the average rate of change from x = 0 to x = 3.

This is because:

slope = rise/run = (change in y)/(change in x) = average rate of change.

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Now let's find the slope for the table.

Focus on the rows for x = 0 and x = 3. They lead to f(x) = 10 and f(x) = 4 respectively.

We have (0,10) and (3,4) as our two points this time.

$(x_1,y_1) = (0,10) \text{ and } (x_2,y_2) = (3,4)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{4 - 10}{3 - 0}\\\\m = \frac{-6}{3}\\\\m = -2$

We get the same slope as before, so we have the same rate of change.

Notice the change in y (-6) is the same as before. So we could pick any two y values we want as long as there's a gap of 6 between them, and the second y value is smaller than the first.