Average Rate of Change & Comparing Function Tables

Front

What is the average rate of change?

Back

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.

Front

How do you calculate the average rate of change between two points?

Back

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

Front

What does a linear function look like in a table of values?

Back

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.

Front

What does a quadratic function look like in a table of values?

Back

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

Front

What does an exponential function look like in a table of values?

Back

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

Front

Calculate the average rate of change from 20 to 40 minutes if the values are [10, 20, 30, 40] gallons.

Back

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

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

The average rate of change is 75 ft per hour.

Front

What is the average rate of change of the function values [1, 5]?

Back

The average rate of change is -0.75.

Front

What is the difference between linear and quadratic functions?

Back

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

Front

What is a function table?

Back

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