Question 1051882
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A function has symmetry about the *[tex \Large y]-axis if the point *[tex \Large (a,-b)] is on the graph whenever the point *[tex \Large (a,b)] is on the graph.


A function has symmetry about the origin if the point *[tex \Large (-a,-b)] is on the graph whenever the point *[tex \Large (a,b)] is on the graph.


With the exception of the constant function *[tex \Large y\ =\ 0], a relation that has symmetry about the *[tex \Large x]-axis is not a function.


So, substitute *[tex \Large -f(x)] for *[tex \Large f(x)].  If you have an equivalent function, then you have symmetry about the *[tex \Large y]-axis. Otherwise not.


Substitute *[tex \Large -f(x)] for *[tex \Large f(x)] and *[tex \Large -x] for *[tex \Large x].  If the result is an equivalent function, then you have symmetry about the origin.  Otherwise, not.


Note:  Most functions are not symmetrical about anything.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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