1. Warm up 1.a. Write the explicit formula for the following sequence -2, 3, 8, 13,… b. Find a 10 2.a. Write the recursive formula for the following sequence 2, 8, 14, 20, … b. Find the 40 th term.

2. The graph below represents Maria’s distance from home one day as she rode her bike to meet friends and do a couple of errands for her mom before returning home. 1.What do the horizontal lines on the graph represent? 2.Where in the graph shows her taking care of the 2 errands? 3.Compare how she traveled at the beginning to how she traveled at the very end. 4.Create Maria’s story so that it matches the graph.

3. Characteristics of Functions

4. InterceptsIntercepts x-intercept – the point at which the line intersects the x-axis at (x, 0) y-intercept – the point at which the line intersects the y-axis at (0, y)

5. Find the x and y intercepts, then graph. -3x + 2y = 12

6. Find the x and y intercepts, then graph. 4x - 5y = 20

7. Increasing, Decreasing, or Constant Sweep from left to right and notice what happens to the y-values Finger Test- as you move your finger from left to right is it going up or down? Increasing goes up (L to R) Decreasing falls down (L to R) Constant is a horizontal graph

8. Continuous vs Discrete Continuous has NO breaks Discrete has gaps or breaks

9. ExtremaExtrema Maximum Point – greatest value of the function Minimum Point – least value of the function

10. Domain & Range Domain – all x-values of a function Range – all y-values of a function

11. NotationNotation Interval – represents an interval as a pair of numbers. The numbers are the endpoints of the interval. Parentheses and/or brackets are used to show whether the endpoints are excluded or included Set – using inequalities to describe the values

12. CharacteristicsCharacteristics 1.Domain: 2.Range: 3.Intercepts: 4.Increasing or Decreasing? 5.Maximum or Minimum?

13. Average Rate of Change

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

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

16. 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

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

18. Average Rate of Change using function notation

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

20. f(x) = -4x + 10 from [-1, 3]. m = -4 Ex 2 Find the Average Rate of Change

21. A. Find the rate of change from day 1 to 2. m = 11 Ex 3 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.

22. 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 4 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.

23. ClassworkClasswork Characteristics of Functions

24. HomeworkHomework Rate of Change