Front

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

Back

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

Front

How do you calculate the average rate of change using a graph?

Back

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

Front

What is the average rate of change of the function f(x) = 2x^2 + 12x + 16 on the interval [-3, -2]?

Back

The average rate of change is 2.

Front

If the average rate of change is negative, what does that indicate about the function's behavior over that interval?

Back

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

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 the output does not change regardless of the input.

Front

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

Back

The average rate of change can represent the speed of an object, the growth rate of a population, or any other scenario where change is measured over time.

Front

What is the significance of the average rate of change in calculus?

Back

In calculus, the average rate of change is a precursor to the concept of the derivative, which represents the instantaneous rate of change.

Front

How do 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).

Front

What does it mean if the average rate of change is zero over an interval?

Back

If the average rate of change is zero, it means the function's output remains constant over that interval.

Front

Can the average rate of change be a fraction?

Back

Yes, the average rate of change can be a fraction, indicating a change in output relative to a change in input.