EVEN FUNCTION
A function is even if replacing x with -x does not change the original function.
The graph of an even function is symmetric about the y-axis.
Since f(-x) = f(x); point (x,y) share the same y value as point (-x,y).
example:
*notice points (3,3) and (-3,3) and also note how it is symmetric about the y-axis.
ODD FUNCTION
A function is odd if replacing x with -x results in changing all terms of the original function. The graph of an odd function is symmetric about the origin(0.0).
Since f(-X) = -f(x); point (x,y) lies on the graph only if (-x,-y) lies on the graph.
example:
* Note how it is symmetric about (0,0)
*Figure 5 is an Even Function, Figure 6 is an Odd Function
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"Since f(-x) = f(x); point (x,y) share the same y value as point (-x,y)."
ReplyDelete"Since f(-X) = -f(x); point (x,y) lies on the graph only if (-x,-y) lies on the graph."
How did you move from function form such as f(-x)=f(x) to the two coordinate form of (x, y) and (-x, y)? This jump was a little sudden in your explanation, but other than that, this looks great Wendy! How are you making all these graphs?
i googled the graphs
ReplyDeleteNice explanation Wendy
ReplyDeletekinda gave me a better idea of what odd and even functions are
Wendy!
ReplyDeleteVeryy straightforward and easy to comprehend :D
I like your graph "notes"
Nice explanation! I like the graphs you used too.
ReplyDeleteHey, doesn't f(x)=x^3 remind you of Ms.Hwang's clock?? XD