Average Rate of Change

Front

What is the average rate of change of a function f(x) on the interval [a, b]?

Back

The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (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 for f(x) = 2x^2 + 12x + 16 on the interval [-3, -2]?

Back

First, calculate f(-3) and f(-2). Then use the formula: (f(-2) - f(-3)) / (-2 - (-3)). The answer is 2.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does a positive average rate of change indicate about a function on an interval?

Back

A positive average rate of change indicates that the function is increasing on that interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does a negative average rate of change indicate about a function on an interval?

Back

A negative average rate of change indicates that the function is decreasing on that interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If f(x) = 2x^2 + 3x - 1, what is the average rate of change from x = 1 to x = 2?

Back

Calculate f(1) and f(2), then use the formula: (f(2) - f(1)) / (2 - 1). The answer is 9.

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

How can you find the average rate of change using a graph?

Back

To find the average rate of change using a graph, identify two points on the curve, (x1, y1) and (x2, y2), and use the formula: (y2 - y1) / (x2 - x1).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the significance of the average rate of change in real-world applications?

Back

The average rate of change can represent speed, growth rate, or any change in quantity over time, making it useful in various real-world contexts.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of Mrs. Gordon's movement from 0 to 2 seconds if she travels 5 feet?

Back

The average rate of change is calculated as distance/time = 5 feet / 2 seconds = 2.5 feet per second.

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 always 0, as there is no change in output regardless of the input.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6