1. Warm Up Find the following: (f + g)(-1) = (g f)(x) = (g - f)(2) = (f /g)(x) =

2. Even & Odd Functions March 6 th, 2014

3. What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

4. What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

5. What are even & odd functions? Plug in 3 to this equation… Now plug in -3… What do you notice about the answers?

6. Even Functions A function is even when it is symmetric about the y-axis. Meaning when you plug in –x the function simplifies to be the same f(-x) = f(x) Examples:

7. Odd Functions A function is odd when it is symmetric about the origin - the point (0,0) Meaning when you plug in –x & simplify the signs of each term changes! f(-x) = - f(x) Examples:

8. Functions that are NEITHER A function is neither when it is NOT symmetric about the y-axis or the origin Most functions are neither even nor odd Meaning when you plug in –x you get a completely different function that is not the same & does not have all signs changed Examples:

9. Even Functions-Graphing

10. Even Functions Graphing Determine which are even…

11. Odd Functions-Graphing

12. Odd Functions Graphing Determine which are odd…

13. Even Functions-Algebraically Plug in –x and simplify! If you get the same function, it is even!

14. Odd Functions-Algebraically Plug in –x and simplify! If you get the opposite function, it is odd!

15. Neither Functions-Algebraically Plug in –x and simplify! If you do not get the same function, or all of the signs do not change, it is neither! If the function has a mixture of even or odd exponents, or odd exponents & a constant then it will be neither! This is the MOST COMMON! Still -5

16. Example:

21. Determine if the function is even, odd, or neither.

22. Example: Determine if the function is even, odd, or neither.

23. Example: Determine if the function is even, odd, or neither.

24. Example: Determine if the function is even, odd, or neither.

25. Example: Determine if the function is even, odd, or neither.

26. Example: Determine if the function is even, odd, or neither.

27. Example: Determine if the function is even, odd, or neither.

28. Example: Determine if the function is even, odd, or neither.

29. NC Final Exam Question Example Which of the following is an even function?

30. Challenge Question Is (x+1) 2 even, odd, or neither?

31. Challenge Question Can a function be both even and odd?

32. Classwork Complete side 1 of the worksheet the graphs #1-11, and #12-19

33. Homework Complete the back side of the worksheet! Graphs & multiple choice questions from http://www.mathsisfun.com/algebra/functions-odd-even.html http://www.mathsisfun.com/algebra/functions-odd-even.html