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

2. Average Rate of Change

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

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

5. 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

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

7. 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

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

9. 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

10. 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

11. Average Rate of Change

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

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

14. You Try!! Find the average rate of change for f(x) = x 2 + 2 from [-3, 5].

15. 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) 119 230 348 476 5121 6192 B. Find the rate of change from day 2 to 5.

16. In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011. m = -5 Ex 5 Find the Average Rate of Change Year (x)Households in Millions f(x) 200866 200961 201056 201151 What does this mean? It decreased 5 million households per year from 2008 – 11.