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

2. Even & Odd Functions

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. So Basically… Plug in a negative and get Same # Different Signs  Odd
Plug in a negative and get a
Same Number Same Sign  Even

10. Even Functions-Graphing

11. Even Functions Graphing Determine which are even…

12. Odd Functions-Graphing

13. Odd Functions Graphing Determine which are odd…

14. Even Functions-Algebraically
Plug in –x and simplify!
If you get the same function, it is even!
Note: If the function has all EVEN exponents and/or a constant (#) it will be even! That means it has variable exponents of 2,4,6,etc…

15. Odd Functions-Algebraically
Plug in –x and simplify!
If you get the opposite function, it is odd!
Note: If the function has all ODD exponents & NO constant it will be odd! That means EVERY variable term has an exponent of 1,3,5,7,etc…

16. 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!
Still -5
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!

17. Example:

18. Example:

19. Example:

20. Example:

21. Example:

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

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

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

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

33. Homework Worksheet front and back! Don’t forget to Justify!!!
Graphs & multiple choice questions from