Warm up 1.What is the tenth term of a n = 2n + 3? 2. What is the Domain: Range: x – ints: y – int:

Average Rate of Change

Rate of Change Ratio describing how one quantity changes as another quantity changes Slope can be used to describe it

Rate of Change Positive – increases over time Negative – decreases over time

Rate of Change Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time

Rate of Change Horizontal lines have 0 rate of change Vertical lines have undefined rate of change

The slope of a non-vertical line is the ratio of the vertical change (change in y) to the horizontal change (change in x) between any two points on the line. Rate of Change

Example: Find the slope between Example: Find the slope between (2, 4) and (4, 8)(2, 4) and (4, 8) Rate of Change

Example: The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change between 2 hours and 6 hours. Example: The table shows the amount of water evaporating from a swimming pool on a hot day. Find the rate of change between 2 hours and 6 hours. Rate of Change

Example: Where is the greatest rate of change on the graph? Example: Where is the greatest rate of change on the graph? What is the value? What is the value? Rate of Change

Average Rate of Change

f(x) = -4x + 10 from [-1, 3]. m = -4 Ex 1 Find the Average Rate of Change

Ex 2 Find the Average Rate of Change f(x) = 2x 2 – 3 from [2, 4].

You Try!! Find the average rate of change for f(x) = x from [-3, 5].

A. Find the rate of change from day 1 to 2. m = 11 Ex 4 Find the Average Rate of Change Days (x)Amount of Bacteria f(x) B. Find the rate of change from day 2 to 5.

In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – m = -5 Ex 5 Find the Average Rate of Change Year (x)Households in Millions f(x) What does this mean? It decreased 5 million households per year from 2008 – 11.