Even and Odd Functions

Now presenting my super late blog!! :3

Hehe, funny story... I dreamt i did it... >__>;;

Do not judge me!!

~~

Okay. So we're talking about functions yes? As in:

f(x)= x^2 ...

f(x)=x+3 ...

And so on!

The topic here is telling the difference between odd and even ones... which is pretty confusing for me. But I will try none-the-less to comprehend.

Let's start with even functions!

From what we went over in class I understand that graphically, a function is EVEN when it is symmetrical to the y-axis. Or in other words, when you fold the graph along the y-axis, quadrants 1 & 4 over quadrants 2 & 3, the line of the function will be the same on the opposite side. Like a mirror!

Mathematically the definition of an even function is this:

f(-x) = f(x)

This means that in a function, the output of the f(-x) will be the same as the output of f(x).

[Example; f(2)=6 /and/ f(-2)=6]
But it has to work with all numbers or it won't count!

Some graph examples:

Now for odd functions!!

ODD functions, graphically, are kind of like even functions. BUT they are not symmetrical along the y-axis but at the origin!! (0,0) Lol, for some reason odd functions remind me of Ms. Hwang's clock x]

The mathematical definition of an odd functions is this:

f(-x)=-f(x)

This in particular means that in a function, the output of f(-x) will result the same output of f(x) unit wise but the direction in which it's going is in the opposite direction.
[Example; f(2)=6 /and/ f(-2)=-6]

Just like the even function, this has to work with all numbers used as the input.

Some graph examples of odd functions:

One other thing that I forgot to mention, a function is 'neither' if it does meet either requirements for even and odd functions.
... Yeah, guess that's about it... ^^;

Well, that's all folks!!

Happy Monday everyone! :D

[Yes, I remembered it's not Tuesday...]