1. Warm-up Given: Evaluate: 1.f (-1) 2.- f (x) 3.f (-x) 4.Determine the difference quotient

2. Practice

3. HW prob. p. 76 #10 HW prob. p. 76 #10

4. 2.3 Properties of Functions Agenda Feb. 12 HW Check Questions Lesson 2.3 – part 1 Quiz Finish Lesson 2.3

5. 1. Definition: Increasing/Decreasing/Constant

6. Increasing/Decreasing/Max/Min Use x-intervals to describe: 1)Increasing : 2)Decreasing: 3)Constant Use x-intervals to describe: 1)Increasing : 2)Decreasing: 3)Constant

7. Increasing/Decreasing/Max/Min Local (relative) maximum : “peaks/high” points Local (relative) minimum: “valleys/low” points Local (relative) maximum : “peaks/high” points Local (relative) minimum: “valleys/low” points

8. Local Minima and Maxima List intervals of increasing/decreasing and all maxima/minima. p. 89 #12.

9. 5. Symmetry Some functions have graphs with symmetry: Even function symmetry with respect to y-axis ODD function symmetry with respect to origin no symmetry

10. 5) Even and Odd Functions To prove a function is EVEN Show: To show algebraically ODD Show: Even function symmetry with respect to y-axis Odd function symmetry with respect to origin

11. 5 b) Examples. Determine if even/odd Determine whether the following functions are even, odd, or neither. Then state any symmetry (origin/y-axis) 1) 2) 3) 4)

12. 4 a) Using the Graphing Calculator 1. Approximate local maxima or minima. 2. Increasing/Decreasing

13. 6. Average Rate of Change Average rate of change from a to b is Secant Line ab

14. 6 a) Example: Find Average Rate of Change a)Find the average rate of change from -2 to 6. b)Find the equation of the secant line connecting the points. Average rate of change

15. Homework 24 p. 88 # 21, 26, 31, 33-36, 42, 43, 45, 48, 55, 65 Finish p. 76 # 24, 25 (from yesterday's homework)

16. 5) Even and Odd Functions Is the same as ? Evaluate and simplify: Evaluate : Even function Is the same as ? ODD function neither YES NO YES NO

17. Example: Given height at time t as: Find average velocity from t = 2 to t = 3 Example: Given height at time t as: Find average velocity from t = 2 to t = 3 6 b) Average Velocity Given: A function rule that determines distance as a function of time. Average velocity is the average rate of change.

18. 6. Average Rate of Change Find the average rate of change from 5 to 16. 516 7– 3 16 – 5