Question

The graph of f(x) = 2x + 1 passes through the points (-1, 1) and (3, 16). Rebecca wants to find the average rate of change from x = -1 to x = 3. Here is her work:

3 - (-1) / (16 - 1) = 4 / 15.

a) Explain Rebecca's error.
a) Rebecca incorrectly calculated the change in x.
b) Rebecca incorrectly calculated the change in y.
c) Rebecca correctly calculated the average rate of change.
d) Rebecca's error is not specified in the options.

Answer 1

Rebecca made a mistake in her calculation by switching the numerator and the denominator. The correct average rate of change calculation for the function f(x) = 2x + 1 from x = -1 to x = 3 is (16 - 1) / (3 - (-1)), which equals 15 / 4 or 3.75. Rebecca's error lies in incorrectly calculating the change in y.

Step-by-step explanation:

Rebecca wants to find the average rate of change of the function f(x) = 2x + 1 from x = -1 to x = 3. Her calculation, however, is incorrect. The average rate of change should be calculated by finding the change in y values divided by the change in x values. Hence, the correct calculation is: (f(3) - f(-1)) / (3 - (-1))

Using the points given, (-1, 1) and (3, 16), this would be:

(16 - 1) / (3 - (-1))

Which simplifies to: 15 / 4 = 3.75

The error in Rebecca's calculation is that she incorrectly calculated the change in y by reversing the numerator and denominator in her fraction. The correct answer is that Rebecca incorrectly calculated the change in y.