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An even function has this property

f(x)=f(-x)

and an odd function has this property

-f(x) = f(-x)

- Thread starter eax
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An even function has this property

f(x)=f(-x)

and an odd function has this property

-f(x) = f(-x)

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Yes. Note that many functions are neither even nor odd.

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Thanks! I just had a test, and one question said to give an example of an odd function and another to prove a function is odd. I looked at the "prove" question and guessed correctly :).hypermorphism said:Yes. Note that many functions are neither even nor odd.

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symetry can be of 4 types:eax said:Thanks! I just had a test, and one question said to give an example of an odd function and another to prove a function is odd. I looked at the "prove" question and guessed correctly :).

on the x-axis (like y^2-x^2=0 or the equation of an elipse etc)

on the y-axis (like y=x^2 or a function with even degree - hence it's an "even" function)

on the origin (meaning that if point (1,5) and (2,10) belong to it so must points (-1,-5) and (-2,-10)...in other words it is copied inversed in the negative direction)

on the y=x axis (like any function and it's inverse or like y=x+1 and y=x-1 for example)

i think the "odd" function is that symetric on orrigin i don't remember.

there are functions that are not symetric to anything. example: e^(-x)Sin(x^3). it would be just a function oscilating back and forth across the x-axis and ending up in a horisontal asymptote at y=0.

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odd functions have rotational symmetry; even functions have reflectional(?) symmetry

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OF course, "even" and "odd" applies to other functions as well: sin(x) is an odd function and cos(x) is an even function.

Given any function, f(x), we can define the "even" and "odd" parts of f by

[tex]f_{odd}(x)= \frac{f(x)- f(-x)}{2}[/tex]

[tex]f_{even}(x)= \frac{f(x)+ f(-x)}{2}[/tex]

If f(x)= e

f

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