4. Even and Odd Functions madelinemontavon.cmswiki.wikispaces.net
September 30th

5. What are even & odd functions?!
Plug 3 into this equation:
2x4 – 3x2 + 1 =
No plug -3 into this equation:
What do you notice about these answers?

6. What are even & odd functions?!
Plug 3 into this equation:
2x3 – 3x =
No plug -3 into this equation:
What do you notice about these answers?

7. What are even & odd functions?!
Plug 3 into this equation:
2x2 – 3x – 1 =
No plug -3 into this equation:
What do you notice about these answers?

8. 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:
1. x2 – x x4 + x2

9. Odd Functions
A function is odd when it is symmetric about the origin – the point (0, 0).
Meaning when you plug in (-x) and simplify the signs of each term changes:
f(-x) = -f(x)
Examples:
1. x3 – x x5 + x x3

10. Functions that are NEITHER Odd nor Even
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 and does not have all signs changed:
Examples:
1. x3 – x x4 + x x3 + 5x – 4

11. Even Functions - Graphing

12. Even Functions – Graphing Determine which are even…

13. Odd Functions - Graphing

14. Odd Functions Graphing Determine which are odd…

15. 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…

16. 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…

17. 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!

18. Example

19. Example

20. Example

21. Example

22. Example

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

28. Challenge Question 1. Is (x+1)2 even, odd, or neither?
2. Can a function be both even and odd?

29. Classwork
Complete the front of the worksheet with a partner

30. Homework Complete Worksheet Need more help? Check out this website:
odd-even.html
ctions_and_graphs/analyzing_functions/v/recognizi ng-odd-and-even-functions