Period 4: Odd and Even Functions

Odd Functions

Graphically:

- We reflect the function f(x) first in the y-axis, then in the x-axis, so we reflect it twice on two axis, and we can say that the function is odd.

-After that we can check by rotating the function 180 degrees about the origin!

f(x) = x^9 is a typical odd function because the degree is odd

Algebraically:

f(x) = 3x^9
f(-x) = 3(-x)^9
f(-x) = -3^9

it does not equal to f(x) so it is an odd function!
-Remember: a function can not be odd and even at the same time!

Even Functions

Graphically:

- We reflect the function f(x) in the y-axis, and it is identical to the original graph, and the graph is even.

Algebraically:

f(x) = x^4
f(-x) = (-x)^4
f(-x) = x^4

f(-x) = f(x)

Because any number no matter positive or negative, to the power of an even number, it will turn positive, therefore it will be identical to the original function.