There are two types of symmetry that the graph of a function can have — even or odd. A function has even symmetry if it is symmetric with respect to the -axis. In other words, if the -axis cuts the graph into two mirror images.
Notice that if the graph were folded vertically on the -axis, the marked points would lie on top of each other. This is true for every point on Thus, has even symmetry. A function is said to have odd symmetry if it's symmetric about the origin. In other words, if one half of the graph can be rotated to match the other half of the graph exactly.
Notice that the portion of the graph below the -axis could be rotated so that it lies directly on top of the portion above the -axis. Thus, has odd symmetry.