1. Power Functions
Investigating symmetry to determine if a power function is even, odd, or neither.

2. Even and Odd Functions (algebraically)
A function is even if f(-x) = f(x)
If you plug in x and -x and get the same solution, then it’s even.
Also: It is symmetrical over the y-axis.
The easiest thing to do is to plug in 1 and -1 (or 2 and -2)
if you get the same y, then it’s Even.
If you get the opposite y, then it’s Odd.
If you get different y’s, then it’s Neither.
A function is odd if f(-x) = -f(x)
If you plug in x and -x and get opposite solutions, then it’s odd.
Also: It is symmetrical over the origin

3. Y – Axis Symmetry Fold the y-axis
Even Function
(x, y)  (-x, y) -5 1 -4 2 -1 3 4 4 11 -1 -4 -2 -3
(x, y)  (-x, y)

4. Test for an Even Function
A function y = f(x) is even if , for each x in the domain of f.
f(-x) = f(x)
Symmetry with respect to the y-axis

5. Symmetry with respect to the origin
(x, y)  (-x, -y)
(2, 2)  (-2, -2)
(1, -2)  (-1, 2)
Odd Function

6. Test for an Odd Function
A function y = f(x) is odd if , for each x in the domain of f.
f(-x) = -f(x)
Symmetry with respect to the Origin

7. Ex. 1
Even, Odd or Neither?
Graphically
Algebraically
ODD

8. Ex. 2
Even, Odd or Neither?
Graphically
Algebraically
EVEN

9. Ex. 3
Even, Odd or Neither?
Graphically
Algebraically
Neither

10. Even functions are symmetric about the y-axis
What do you notice about the graphs of even functions?
Even functions are symmetric about the y-axis

11. Odd functions are symmetric about the origin
What do you notice about the graphs of odd functions?
Odd functions are symmetric about the origin

12. EVEN

13. Neither

14. Neither

15. EVEN

16. ODD

17. Neither

18. EVEN