Even and Odd Functions

From RaVPup's Notes

Even and odd functions get their name from the fact that even functions only contain even powers and odd functions only contain odd powers. Even functions can be reflected around the y-axis without losing symmetry and odd functions can be reflected around the origin (x-axis) without losing symmetry. From this definition, we are able to make a statement about the evenness or oddness of products and quotients of these functions based on these rules

\frac{even}{even} = even

\frac{even}{odd} = odd

\frac{odd}{odd} = even

\frac{odd}{even} = odd

even \times even = even \

even \times odd = odd \

odd \times odd = even \

odd \times even = odd \

The function x2 is an even function with its graph shown below.

Image:x^2.gif

The function x3 is an odd function with it's graph shown below.

Image:x^3.gif

The function \frac{x^2}{x^3} is odd function, with it's graph shown below.

Image:1onx.gif

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