Ok, from what i understood, this is my answer.
Even functions are those that have an even power to the x. They are symmetrical about the y-axis because the inputs are the opposites of each other along the x-axis but the output, which is y, will be the same due to the fact that a negative times a negative will always equal a positive [ex. (-x)^2 Is the same as -x*-x]. So, for example, the points on the 1st quadrant and the 4Th quadrant would be symmetrical about the y-axis. Therefore f(-x)=f(x).
Odd functions are those with an odd power to the x. An odd function is represented with this equation: f(-x) = -f(x)
For example, if a point (1,1) lies on a graph, then the opposite points (-1,-1) must also lie on that graph. If (-1, 1) lies on a graph then you will also find (1,-1). So it reflects twice you could say. If the function was originally on the 1st quadrant it will reflect about the y axis and then again about the x axis making is symmetrical about the origin.
Posted on SATURDAY @ 4
Have a nice weekend guys
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"Even functions are those that have an even power TO THE X"
ReplyDeleteBe careful how you say this. "to the x" means to the power of x.
Your even explanation is great. A graph like y=cos x is also even though that you don't take into consideration.
For your odd explanation, make sure you connect your examples to the actual equation, f(-x)=-f(x)