Average Rate of Change NYS Regents Practice

Front

What is the Average Rate of Change?

Back

The Average Rate of Change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you calculate the Average Rate of Change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where [a, b] is the interval.

Front

What does a positive Average Rate of Change indicate?

Back

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

Front

What does a negative Average Rate of Change indicate?

Back

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

Front

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

Back

It helps in understanding how quantities change over time, such as speed, growth rates, and economic changes.

Front

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

Back

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

Front

What is the Average Rate of Change of a constant function?

Back

The Average Rate of Change of a constant function is 0, as there is no change in the function's value.

Front

How does the Average Rate of Change relate to the slope of a line?

Back

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

Front

What is the Average Rate of Change of the function f(x) = x^2 from x = 2 to x = 3?

Back

Average Rate of Change = (f(3) - f(2)) / (3 - 2) = (9 - 4) / 1 = 5.

Front

What is the Average Rate of Change of the function f(x) = -x + 5 from x = 0 to x = 5?

Back

Average Rate of Change = (f(5) - f(0)) / (5 - 0) = (0 - 5) / 5 = -1.