Average Rate of Change

Front

What is the Average Rate of Change (ARC)?

Back

The Average Rate of Change is a measure of how much a function's output value changes, on average, for a given change in the input value over an interval.

Front

What is the formula for calculating the Average Rate of Change?

Back

The formula is: ARC = (y2 - y1) / (x2 - x1)

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 1.

Front

How do you find the average rate of change from a graph?

Back

Identify two points on the graph (x1, y1) and (x2, y2) and use the formula ARC = (y2 - y1) / (x2 - x1).

Front

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

Back

It indicates that the function is increasing over the interval.

Front

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

Back

It indicates that the function is decreasing over the interval.

Front

What is the average rate of change of f(x) = x^2 on the interval [1, 3]?

Back

The average rate of change is 4.

Front

If the average rate of change is zero, what does that imply about the function?

Back

It implies that the function is constant over that interval.

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 -2.

Front

How can you interpret the average rate of change in a real-world context?

Back

It can represent speed, growth rate, or any change in quantity over time.