The power function f ( x ) = x n is an even function if n is even and n ≠ 0 , and it is an odd function if n is odd Even functions are symmetric about the y -axis whereas odd functions are symmetric about the origin

The root function f ( x ) = x 1 / n has the domain [ 0 , ∞ ) if n is even and the domain ( -∞ , ∞ ) if n is odd. If no domain is stated for a function y = f ( x ) , the domain is considered to be the set of all real numbers x for which the function is defined

function — a set of inputs, a set of outputs, and a rule for mapping each input to exactly one output. graph of a function — the set of points ( x , y ) such that x is in the domain of f and y = f ( x ). odd function — a function is odd if f ( - x ) = - f ( x ) for all x in the domain of f. even function — a function is even if f ( - x ) = f ( x ) for all x in the domain of f.