Final answer:
The correct statement for an even function is f(-x) = f(x), showing that the function is unchanged when x is replaced by -x and such a function has symmetry about the y-axis.
Step-by-step explanation:
If a function is even, then the correct completion of the statement is f(-x) = f(x), which means that for an even function, the value of the function at x is the same as at -x. Moreover, an even function has symmetry about the y-axis. This is indicative of a typical property of even functions where if you fold the graph along the y-axis, the two halves will align perfectly, demonstrating this symmetry.
Reflecting on the choices provided, the correct answer is A) f(x) = f(-x); the y-axis, because it correctly states the condition for a function to be even and indicates the axis about which the function is symmetrical. Examples of even functions include x2, cos(x), and any other function where the graph on one side of the y-axis is a mirror image of the graph on the other side.