Average Rate of Change & Comparing Function Tables

The average rate of change is a measure of how much a quantity changes on average over a specific interval. It is calculated by dividing the change in the value of the function by the change in the input value.

To calculate the average rate of change between two points (x1, y1) and (x2, y2), use the formula: (y2 - y1) / (x2 - x1).

A linear function has a constant rate of change, meaning the difference between consecutive y-values divided by the difference in x-values is the same.

A quadratic function shows a pattern where the second differences of the y-values are constant, indicating a parabolic shape.

An exponential function shows a pattern where the ratio of consecutive y-values is constant, indicating rapid growth or decay.

The average rate of change is -2 gallons per minute.

The average rate of change is 75 ft per hour.

The average rate of change is -0.75.

Linear functions have a constant rate of change, while quadratic functions have a variable rate of change that forms a parabola.

A function table is a way to organize input (x) and output (y) values of a function to analyze its behavior.