Average Rate of Change NYS Regents Practice

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What is the Average Rate of Change?

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The Average Rate of Change of a function over an interval [a, b] is defined as the change in the function's value divided by the change in the input value, calculated as (f(b) - f(a)) / (b - a).

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How do you calculate the Average Rate of Change?

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To calculate the Average Rate of Change, use the formula: (f(b) - f(a)) / (b - a), where f(b) is the function value at point b and f(a) is the function value at point a.

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What does a positive Average Rate of Change indicate?

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A positive Average Rate of Change indicates that the function is increasing over the interval.

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What does a negative Average Rate of Change indicate?

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A negative Average Rate of Change indicates that the function is decreasing over the interval.

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What does an Average Rate of Change of zero indicate?

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An Average Rate of Change of zero indicates that the function is constant over the interval.

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If f(x) = 2x + 3, what is the Average Rate of Change from x = 1 to x = 4?

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The Average Rate of Change is (f(4) - f(1)) / (4 - 1) = (11 - 5) / 3 = 2.

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What is the significance of the Average Rate of Change in real-world applications?

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The Average Rate of Change can represent speed, growth rate, or any change over time, making it useful in fields like physics, economics, and biology.

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How can you interpret the Average Rate of Change graphically?

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Graphically, the Average Rate of Change corresponds to the slope of the secant line connecting two points on the graph of the function.

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What is the relationship between Average Rate of Change and instantaneous rate of change?

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The Average Rate of Change over an interval approaches the instantaneous rate of change at a point as the interval shrinks to zero.

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What is a secant line?

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A secant line is a line that intersects a curve at two or more points, representing the Average Rate of Change between those points.