Rate of Change

Front

What is the rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity. It is often expressed as a ratio or a fraction.

Front

How do you calculate the average rate of change?

Back

The average rate of change between two points is calculated by taking the difference in the values of the function at those points and dividing it by the difference in the input values.

Front

What is the formula for average rate of change?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a), where f(b) and f(a) are the function values at points b and a.

Front

What does a positive rate of change indicate?

Back

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

Front

What does a negative rate of change indicate?

Back

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

Front

What is a constant rate of change?

Back

A constant rate of change means that the quantity changes by the same amount over equal intervals.

Front

If the rate of change is zero, what does it mean?

Back

If the rate of change is zero, it means that the quantity is constant and does not change over the interval.

Front

Example: Find the average rate of change from 3 to 6 if the values are 10 and 15.

Back

Average Rate of Change = (15 - 10) / (6 - 3) = 5 / 3 = 1.67.

Front

What is the significance of the slope in a graph?

Back

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

Front

How can you interpret a steep slope?

Back

A steep slope indicates a rapid rate of change, meaning the quantity is changing quickly.