Graphs of Odd and Even Functions

Recall the following definition of an even function:

A function  f is even if  $f(x)=f(-x)$ for all x in the domain of  f.

The pair of points $(x,y)$ and $(-x,y)$ are ordered pairs that satisfy the given function. These ordered pairs represent points on the graph of the function. Observe that x and $-x$ are paired with the same value of y. This causes the graph to be symmetric with respect to the y-axis. So if you draw a graph on a piece of paper and fold it along the y-axis, the right part of the graph will coincide with the left. The right part of the graph is the mirror image of the left. Thus, an even function is symmetric with respect to the y-axis.

The pair of points $(x,y)$ and $(-x,-y)$ are ordered pairs that satisfy the given function. These ordered pairs represent points on the graph of the function. Observe that $(x,y)$ and $(-x,-y)$ are reflections of one another about the origin. This means that the points are of the same distance from the origin and lie on a single line through the origin. Thus, an odd function is symmetric with respect to the origin.