Domain and Range Calculator

About this calculator

The domain of a function is the complete set of input values (x) for which it is defined, and the range is the complete set of output values (y) it can produce — together they describe exactly what a function can accept and what it can return, which is foundational before graphing, composing, or inverting a function.

Each common function type has a characteristic domain and range shape: a linear function (y = mx + b, m ≠ 0) has all real numbers for both; a quadratic (y = ax² + bx + c) has all reals as domain but a range bounded above or below by its vertex depending on the sign of a; a square root function is restricted to inputs that keep the radicand non-negative, giving a range of non-negative outputs (or the reverse, depending on orientation); and a reciprocal function (y = a/x) excludes x = 0 from the domain and y = 0 from the range, since division by zero and a zero numerator are impossible or excluded respectively. This calculator identifies the domain and range for a chosen function type from its coefficient and constant.