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 (180⁰ 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 2nd TRACE (calc) 4:maximum (-2,0)

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

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

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

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

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