Even and Odd functions have their similarities and their differences, a similarity is that both even and odd functions have corresponding coordinates on either side of the Y-axis. These functions are different because even functions are always symmetrical, while odd functions are not. Odd functions however would look symmetrical if either the right or left side of the graph is flipped over the X-axis. Below, to the left is an example of an even function and to the right is an odd function.
A rule for even functions is that for every (x, f(x)) there is a corresponding (-x, f(x)). A rule for odd functions is that for every (x, f(x)) there is a corresponding (-x, -f(x)). This is another way to check if it's truly an even or odd function. The functions below show that the points correspond with each other, confirming that the left graph is an even function and that the right graph is an odd function.
The parent functions x^2, x^4, x^6, x^8, etc. are even functions as well as cos(x). The parent functions x^3, x^5, x^7, x^9, etc. are odd functions as well as sin(x). While these functions are even and odd now, they easily can become neither by moving the functions up or down the y-axis.