Domain of a function

A function is given when to each number x from some set a number y is assigned; x is the independent variable (argument), y is the function. The set of all values the argument may take is the domain of the function. For a function given by a formula, the domain is all x for which the formula makes sense. So an expression in a denominator must not be zero, and an expression under an even-degree root (such as a square root) must not be negative. Polynomials (for example quadratic functions) are defined for all real numbers. The function y = |x| is defined for all x: y = x for x ≥ 0 and y = −x for x < 0; its graph is symmetric about the Oy axis and consists of the bisectors of the first and second coordinate angles. The graph of y = |x − 3| − 2 is obtained from y = |x| by shifting 3 units right and 2 units down.