Average rate of change

Front

What is the definition of 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 between two points (x1, y1) and (x2, y2)?

Back

The average rate of change is calculated using the formula: (y2 - y1) / (x2 - x1).

Front

What is the average rate of change of a function if the output decreases as the input increases?

Back

The average rate of change will be negative, indicating a decrease in the function's value.

Front

If a function has an average rate of change of 0 over an interval, what does this imply about the function's behavior?

Back

It implies that the function's value does not change over that interval; it remains constant.

Front

What is the average rate of change of a linear function?

Back

The average rate of change of a linear function is constant and equal to the slope of the line.

Front

How can you represent the average rate of change graphically?

Back

Graphically, the average rate of change can be represented as the slope of the secant line connecting two points on the graph of the function.

Front

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

Back

It helps to understand how one quantity changes in relation to another, such as speed, growth rates, and economic changes.

Front

What is the average rate of change from 1 to 5 if the function values are f(1) = 3 and f(5) = 1?

Back

The average rate of change is (1 - 3) / (5 - 1) = -0.5.

Front

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

Back

Identify two points from the table, then use the formula (y2 - y1) / (x2 - x1) to calculate the average rate of change.

Front

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

Back

A positive average rate of change indicates that the function's value is increasing over the interval.