For even functions the input for an even function is always opposite from the each other. Speaking Mathematically f(-x)=f(x) for even functions. However graphically its just a reflection of a even functions. Even functions are always symmetrical on the Y-axis. When an input is placed ;the Y-axis always stays the same,but the x intercept is opposite from each other. The parent function of X^2 is a perfect example to portray this explanation since placing a input gives you one output.. Which I like to think of as (X,Y)As you can see in the picture, the X-intercept is opposite of each other and the Y-intercept in Quadrant 1 is the same in #2. The Y-intercept is symmetrical.
ODD Functions : Speaking Mathematically a Odd function is defined as f(-x)=-f(x). Odd functions are always symmetrical about the origin. Simply put , an even function are opposites of each other like the even function however contain different points. A line is a perfect example to portray an Odd function. Since a line is on the origin and reflects the output as symmetrical points on the graph.As you can see, the line is reflecting on the origin and the points on Quadrant 2 and 3 and the opposite of each other. (X,Y) on Quadrant 2 are all positive , Whereas Quadrant 3 (X,Y) are all negative.
( I GOT THE LINE GRAPH IDEA FROM A FELLOW STUDENT. )
where is the odd?? the even part sounds great!
ReplyDeleteWell written....
ReplyDeleteWhat do you mean by "opposite"? You use it the same way for even and odd functions.
ReplyDelete"the Y-axis always stays the same,but the x intercept is opposite from each other"
I think you're on a great track here, but I think you mean the Y-VALUE always stays the same whiel the X-VALUE is opposite of each other. y-axis and x-intercept mean something totally different and very specific.