1. Warm up Find the domain and range of the following graphs.

2. Coordinate Algebra UNIT QUESTION: How can we use real- world situations to construct and compare linear and exponential models and solve problems? Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5 Today’s Question: How do I find the average rate of change of a function? Standard: MCC9-12.F.IF.6

3. Average Rate of Change

4. Rate of Change of a Linear Relationship The rate of change of a linear relationship is the slope of the line. rise run Rate of Change =

5. Rates of change are seen everywhere.

6. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

7. Give one reason why some homes have roofs which have a greater pitch. There is less snow buildup in the wintertime.

8. Engineers refer to the rate of change of a road as the grade.

9. They often represent the rate of change as a percentage.

10. A grade of 8% would mean for every rise of 8 units there is a run of 100 units. 8 100 = 8% Rate of change =

11. The steepness of wheelchair ramps is of great importance for safety. Rate of change of wheelchair ramp = 1 12 If the rise is 1.5 m, what is the run? Answer: 18 m because

12. 3 m 5 m Determine the rate of change (pitch) of the roof.

13. 2 3 3 3 Determine the rate of change of each staircase.

14. Determine the rate of change. Which points will you use to determine rise and run? = $5/hr 20 4 EarningsEarnings Number of Hours Worked What does this rate of change represent? The hourly wage

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

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

17. 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

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

19. Average Rate of Change

20. Ex 1 Find the Average Rate of Change f(x) = 2x 2 – 3 from [2, 4].

21. Ex 2 Find the Average Rate of Change f(x) = 3 x – 2 from [2, 5].

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

23. 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.

24. 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.