Graded - Average Rate of Change of Non-Linear Functions

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 determine if a function is linear?

Back

A function is linear if its graph is a straight line, which means the rate of change is constant throughout the interval.

Front

What is a non-linear function?

Back

A non-linear function is a function whose graph is not a straight line, indicating that the rate of change varies over the interval.

Front

What does a negative average rate of change indicate?

Back

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

Front

What does a positive average rate of change indicate?

Back

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

Front

How can you visually identify a non-linear function on a graph?

Back

A non-linear function can be identified by its curved graph, which does not form a straight line.

Front

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

Back

The slope of a linear function represents the constant rate of change between the dependent and independent variables.

Front

What is the formula for calculating the slope of a line?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2) on the line.

Front

What is the difference between average rate of change and instantaneous rate of change?

Back

The average rate of change measures the change over an interval, while the instantaneous rate of change measures the change at a specific point.

Front

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

Back

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