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Which has a greater average rate of change -2 ≤ x ≤ 4, g(x) = 16x-3 or f(x)= 2x²

A. g(x) = 16x - 3.
B. f(x) = 2x².

1 Answer

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Final answer:

The function g(x) = 16x - 3 has a greater average rate of change than f(x) = 2x² over the interval -2 ≤ x ≤ 4 because its average rate of change (slope) is 16, compared to 4 for f(x).

Step-by-step explanation:

To determine which function has a greater average rate of change on the interval -2 ≤ x ≤ 4, we can compute the average rate of change for each function over that interval. For g(x) = 16x - 3: The average rate of change is given by the slope of the line, which is 16. For f(x) = 2x²: We find the value of the function at the endpoints of the interval: f(-2) = 2(-2)² = 8 and f(4) = 2(4)² = 32. Then, the average rate of change of f(x) is (f(4) - f(-2)) / (4 - (-2)) = (32 - 8) / (4 + 2) = 24 / 6 = 4. Therefore, the function g(x) = 16x - 3 has a greater average rate of change than f(x) = 2x² over the interval -2 ≤ x ≤ 4, which makes option A correct.

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