11.19.24 Average rate of change

Front

What is the average rate of change of a function over an interval?

Back

The average rate of change of a function over an interval [a, b] is calculated as (f(b) - f(a)) / (b - a).

Front

How do you calculate the rate of change from a graph?

Back

To calculate the rate of change from a graph, identify two points (x1, y1) and (x2, y2) on the graph and use the formula (y2 - y1) / (x2 - x1).

Front

What does a negative rate of change indicate?

Back

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

Front

What is the significance of the slope in a linear graph?

Back

The slope of a linear graph represents the rate of change of the dependent variable with respect to the independent variable.

Front

How can you interpret a rate of change of 0?

Back

A rate of change of 0 indicates that the function is constant over the interval.

Front

What is the formula for calculating the average rate of change between two points?

Back

The formula is (f(x2) - f(x1)) / (x2 - x1), where f(x) is the function value at x.

Front

What does it mean if the average rate of change is positive?

Back

If the average rate of change is positive, it means that the function is increasing over the interval.

Front

How do you determine the units of the rate of change?

Back

The units of the rate of change are determined by the units of the dependent variable divided by the units of the independent variable.

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.

Front

How can you find the average rate of change from a table of values?

Back

To find the average rate of change from a table, select two points (x1, y1) and (x2, y2) and apply the formula (y2 - y1) / (x2 - x1).