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College Algebra - Rate of Change for f(x)











































Average Rate of Change

The rate of change is the slope of a function.

Given the following function: f(x)=10

What is the average rate of change when x = -2 to x = 2 ?

Comments for College Algebra - Rate of Change for f(x)

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Feb 02, 2013
Average Rate of Change
by: Staff


Answer

Since the rate of change of a function is the slope of the function, this problem boils down to calculating the slope.

Slope of Line Between Two Points

slope = "rise" over "run", or "rise" DIVIDED BY "run"

slope = (change in "y" values)/(change in "x" values)

slope = Δy / Δx

slope = (y₂ - y₁)/(x₂ - x₁)



The x-y coordinates of the two points are (-2, 10) and (2, 10).


These points are already listed in the proper order (left to right)

They are listed properly as (-2, 10) and (2, 10) because the slope will be calculated as the change of "y" when x increases. In this case "x" will increase from -2 to 2 (left to right).



Calculation of the slope

Points: Left and Right

(-2, 10) and (2, 10)

(x₁, y₁) and (x₂,y₂)

x₁ = -2
x₂ = 2

y₁ = 10
y₂ = 10

slope = (y₂ - y₁)/(x₂ - x₁)

slope = (10 - 10)/[2 - (-2)]

slope = (10 - 10)/(2 + 2)

slope = (0)/(4)

slope = 0



Final Answer:


                 slope = 0



When the function f(x)=10 is plotted, it is obvious that f(x) is a horizontal, straight line.

Math – Constant Function








Thanks for writing.

Staff
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