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 $y$-axis. In other words, if the $y$-axis cuts the graph into two mirror images.

Notice that if the graph were folded vertically on the $y$-axis, the marked points would lie on top of each other. This is true for every point on $f.$ Thus, $f(x)$ 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 $180^{\circ }$ to match the other half of the graph exactly.

Notice that the portion of the graph below the $y$-axis could be rotated so that it lies directly on top of the portion above the $y$-axis. Thus, $f$ has odd symmetry.