# 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)

 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. Thanks for writing. Staff www.solving-math-problems.com