Select the correct answer.This table represents function f.𝑥-3-2-10123𝑓(𝑥)-4.5-2-0.50-0.5-2-4.5If function g is a quadratic function that contains the points (-3,5) and (0,14), which statement is true over the interval [-3,0]? A. The average rate of change of f is less than the average rate of change of g. B. The average rates of change of f and g cannot be determined from the given information. C. The average rate of change of f is the same as the average rate of change of g. D. The average rate of change of f is more than the average rate of change of g.
Question
Select the correct answer.This table represents function f.𝑥-3-2-10123𝑓(𝑥)-4.5-2-0.50-0.5-2-4.5If function g is a quadratic function that contains the points (-3,5) and (0,14), which statement is true over the interval [-3,0]? A. The average rate of change of f is less than the average rate of change of g. B. The average rates of change of f and g cannot be determined from the given information. C. The average rate of change of f is the same as the average rate of change of g. D. The average rate of change of f is more than the average rate of change of g.
Solution
The average rate of change of a function over an interval [a, b] is given by the formula (f(b) - f(a)) / (b - a).
For function f, over the interval [-3,0], we have: f(0) = 0 f(-3) = -4.5 So, the average rate of change of f is (0 - (-4.5)) / (0 - (-3)) = 4.5 / 3 = 1.5
For function g, we know it contains the points (-3,5) and (0,14). So, over the interval [-3,0], the average rate of change of g is (14 - 5) / (0 - (-3)) = 9 / 3 = 3.
Comparing these, we see that the average rate of change of f (1.5) is less than the average rate of change of g (3).
So, the correct answer is A. The average rate of change of f is less than the average rate of change of g.
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