2.3.1 properties of functions

1. 2.3 Properties of Functions Even, Odd, or Neither (Symmetry) Increasing and Decreasing Intervals Local Maxima and Minima

2. Even Function A function that is symmetric about the y -axis. Algebraically –

3. Odd Function A function that is symmetric about the origin (180 ⁰ rotational symmetry about the origin) Algebraically - same

4. Increasing As the x -values increase, the y -values also increase Describe the x -values in interval notation

5. Decreasing As the x -values increase, the y -values decrease Describe the x -values in interval notation

6. Constant As the x -values increase, the y -value remain the same. Describe the x -values in interval notation

7. Find the intercepts

8. State the Domain and Range

9. Identify the intervals where it is increasing Describe the x -values in interval notation

10. Identify the intervals where it is decreasing Describe the x -values in interval notation

11. Identify the intervals where it is constant None

12. Determine whether it is even, odd, or neither Symmetric about the origin – Odd Function

13. Local Maxima and Minima Local Maximum – The largest value of y on an open interval of x . Local Minima – The smallest value of y on an open interval of x .

14. Identify the local maximum The local maximum is 1, and it occurs when x = π /2

15. Identify the local minimum The local minimum is -1, and it occurs when x = - π /2

16. Identify the local extrema on the given interval (*using a calculator)

17. Find Maximum Estimate an interval of x (-2,0) 2 nd TRACE (calc) 4:maximum

18. Find Maximum (-2,0) 2 nd TRACE (calc) 4:maximum

19. Find Maximum (-2,0) -2 ENTER 0 ENTER ENTER Maximum is 11.53, occurs at x = -.82

20. Find Minimum Estimate an interval of x (0,2) 2 nd TRACE (calc) 3 :minimum

21. Find Minimum (0,2) 0 ENTER 2 ENTER ENTER Minimum is -1.53, occurs at x = .82

22. Assignment p. 88 # 7, 10 - 28 even , 39 - 46 , 63 , 65, 66