The functions f, of, xf(x), g, of, xg(x), and h, of, xh(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval minus, 6, is less than or equal to, x, is less than or equal to, 2−6≤x≤2 goes from least to greatest.f, of, xf(x)-10-8-6-4-224681048121620-4-8-12-16-20xyxx g, of, xg(x)minus, 6−6 8282minus, 2−2 262622 2266 10101010 5050h, of, x, equals, minus, x, squared, minus, 4, x, minus, 20h(x)=−x 2 −4x−20AnswerMultiple Choice Answersg, of, x, comma, f, of, x, comma, h, of, xg(x),f(x),h(x)g, of, x, comma, h, of, x, comma, f, of, xg(x),h(x),f(x)h, of, x, comma, g, of, x, comma, f, of, xh(x),g(x),f(x)f, of, x, comma, g, of, x, comma, h, of, xf(x),g(x),h(x)h, of, x, comma, f, of, x, comma, g, of, xh(x),f(x),g(x)f, of, x, comma, h, of, x, comma, g, of, xf(x),h(x),g(x)
Question
The functions f, of, xf(x), g, of, xg(x), and h, of, xh(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval minus, 6, is less than or equal to, x, is less than or equal to, 2−6≤x≤2 goes from least to greatest.f, of, xf(x)-10-8-6-4-224681048121620-4-8-12-16-20xyxx g, of, xg(x)minus, 6−6 8282minus, 2−2 262622 2266 10101010 5050h, of, x, equals, minus, x, squared, minus, 4, x, minus, 20h(x)=−x 2 −4x−20AnswerMultiple Choice Answersg, of, x, comma, f, of, x, comma, h, of, xg(x),f(x),h(x)g, of, x, comma, h, of, x, comma, f, of, xg(x),h(x),f(x)h, of, x, comma, g, of, x, comma, f, of, xh(x),g(x),f(x)f, of, x, comma, g, of, x, comma, h, of, xf(x),g(x),h(x)h, of, x, comma, f, of, x, comma, g, of, xh(x),f(x),g(x)f, of, x, comma, h, of, x, comma, g, of, xf(x),h(x),g(x)
Solution
The average rate of change of a function on an interval [a, b] is given by the formula (f(b) - f(a)) / (b - a).
Let's calculate the average rate of change for each function on the interval -6 ≤ x ≤ 2:
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For f(x), f(2) = -16 and f(-6) = -4. So, the average rate of change is (-16 - (-4)) / (2 - (-6)) = -12 / 8 = -1.5.
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For g(x), g(2) = 66 and g(-6) = 82. So, the average rate of change is (66 - 82) / (2 - (-6)) = -16 / 8 = -2.
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For h(x), h(x) = -x^2 - 4x - 20. So, h(2) = -4 * 2 - 4 * 2 - 20 = -24 and h(-6) = -4 * 36 - 4 * (-6) - 20 = -144 + 24 - 20 = -140. So, the average rate of change is (-24 - (-140)) / (2 - (-6)) = 116 / 8 = 14.5.
So, the order from least to greatest average rate of change is g(x), f(x), h(x). Therefore, the correct answer is "g, of, x, comma, f, of, x, comma, h, of, x" or "g(x),f(x),h(x)".
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