Which characteristic identifies an even function?

An even function is defined by its symmetry with respect to the y-axis. This means that for every point ( (x, f(x)) ) on the graph of the function, there is a corresponding point ( (-x, f(x)) ). Mathematically, this can be expressed as ( f(x) = f(-x) ) for all ( x ) in the domain of the function. This property leads to a visual representation where the left-hand side of the graph mirrors the right-hand side, creating a balance around the y-axis.

The other options do not define an even function. For instance, while some functions can intersect the x-axis at one point, this characteristic is not unique to even functions and does not provide information about symmetry. Similarly, having a minimum or maximum point is pertinent to specific types of functions but does not relate to the evenness of a function. Therefore, the defining characteristic of an even function remains its symmetry about the y-axis.