"Would be cool to have an im..."

We can think about evenness and oddness in terms of group theory as follows\. There is a group called the cyclic group $C\_2$ of order $2$ acting on all functions\. It has elements which we might call $1$ and $-1$\. $1$ is the identity element: it sends a function to itself\. $-1$ sends a function $f(x)$ to the function $f(-x)$, which visually corresponds to reflecting the graph of $f(x)$ through the y\-axis\. The group multiplication is what the names of the group elements suggests, and in particular $(-1) \\times (-1) \= 1$, which corresponds to the fact that $f(-(-x)) \= f(x)$\.

Would be cool to have an image of an example graph here.