Average Rate of Change

Front

What is the Average Rate of Change?

Back

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).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you calculate the Average Rate of Change?

Back

To calculate the Average Rate of Change, use the formula: (f(b) - f(a)) / (b - a), where f is the function and [a, b] is the interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

For a linear function, the Average Rate of Change is constant and equal to the slope of the line.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

The Average Rate of Change is (f(4) - f(1)) / (4 - 1) = (14 - 5) / 3 = 3.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the Average Rate of Change of the function f(x) = x^2 on the interval [1, 3]?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

The Average Rate of Change over an interval is equivalent to the slope of the secant line that connects the points (a, f(a)) and (b, f(b)).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the Average Rate of Change of f(x) = -2x + 5 from x = 0 to x = 3?

Back

The Average Rate of Change is (f(3) - f(0)) / (3 - 0) = (-1 - 5) / 3 = -2.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6