even function

An even function looks the same on the left and right of the y-axis — its graph is a mirror image folded along that vertical line. Whatever the curve does for positive inputs, it does identically for the matching negative inputs.

The algebraic test is f(-x) = f(x) for every x in the domain. In words, flipping the sign of the input leaves the output unchanged. The name comes from power functions: x^2, x^4, x^6 and other even powers are all even functions, since (-x) raised to an even power equals x raised to that power.

Many functions are neither even nor odd — most are neither. Checking is mechanical: substitute -x for x, simplify, and see whether you get back the original f(x) exactly. If you do, it is even; if you get the exact negative, it is odd; if neither, it is just an ordinary function.