Average Rate of Change

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What is the Average Rate of Change?

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The Average Rate of Change is a measure of how much a quantity changes on average over a specific interval. It is calculated as the change in the value of a function divided by the change in the input value.

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How is the Average Rate of Change calculated?

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The Average Rate of Change is calculated using the formula: (f(b) - f(a)) / (b - a), where f(b) and f(a) are the values of the function at points b and a, respectively.

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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 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 is the slope in the context of a linear function?

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The slope is a measure of the steepness of a line, calculated as the rise (change in y) over the run (change in x). It represents the Average Rate of Change.

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If a function has a slope of -7, what does this mean?

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A slope of -7 means that for every 1 unit increase in x, the value of the function decreases by 7 units.

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What is the Average Rate of Change of a function from 0 to 2 seconds if the distance traveled is 5 feet?

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The Average Rate of Change is 2.5 feet per second, calculated as (5 feet - 0 feet) / (2 seconds - 0 seconds).

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How do you interpret an Average Rate of Change of 4 inches per year for a child's height?

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It means that, on average, the child's height increases by 4 inches for each year of age.

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What is the Average Rate of Change from 20 to 40 minutes if the quantity changes by -40 gallons?

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The Average Rate of Change is -2 gallons per minute, calculated as (-40 gallons) / (20 minutes) = -2 gallons per minute.

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What is the relationship between Average Rate of Change and slope?

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The Average Rate of Change between two points on a graph is equivalent to the slope of the line connecting those two points.