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!
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... ^^;
... Yeah, guess that's about it... ^^;
Well, that's all folks!!
Happy Monday everyone! :D
[Yes, I remembered it's not Tuesday...]
