Answer:
To find the average rate of change for each graph and match it with the corresponding linear function, we need to calculate the slope of each interval and compare it with the given options.
A. For the quadratic function y = x²:
- Interval [-2, -1]: The average rate of change is (f(-1) - f(-2)) / (-1 - (-2)). Calculate the values to find the slope.
- Interval [-1, 0]: Similarly, calculate the average rate of change.
- Interval [0, 1]: Calculate the average rate of change.
- Interval [1, 2]: Calculate the average rate of change.
After calculating the slopes for each interval, we can match them with the given options by comparing the values.
B. For the quadratic function y = -x² + 4x:
- Interval [-2, -1]: Calculate the average rate of change.
- Interval [-1, 0]: Calculate the average rate of change.
- Interval [0, 1]: Calculate the average rate of change.
- Interval [1, 2]: Calculate the average rate of change.
C. For the quadratic function y = x² - 4x:
- Interval [-2, -1]: Calculate the average rate of change.
- Interval [-1, 0]: Calculate the average rate of change.
D. For the quadratic function y = -x²:
- Interval [-2, -1]: Calculate the average rate of change.
- Interval [-1, 0]: Calculate the average rate of change.
- Interval [0, 1]: Calculate the average rate of change.
- Interval [1, 2]: Calculate the average rate of change.
To match the graph of the linear function that represents the average rate of change for each quadratic function, compare the calculated slopes with the given options and find the best match.
Remember to substitute the x-values into the respective quadratic functions to calculate the corresponding y-values and determine the slope correctly.