A function takes an input and produces an output. The domain is the set of all inputs for which the function is defined. For f(x) = 1/x, the domain is all real numbers except zero, because division by zero is undefined. For f(x) = √x, the domain is non-negative numbers if we restrict to real outputs.

The domain can be specified explicitly or implied by the context. In applications, the domain often reflects physical constraints: time cannot be negative, a population cannot be fractional. Mathematicians sometimes restrict the domain to make a function invertible or to simplify analysis.

The range is the set of all outputs. Together, domain and range describe the function's behavior. Understanding both is essential for graphing, solving equations, and modeling real-world problems. The concepts are basic but easily overlooked.

• Set of all valid inputs
• Can be explicit or implied
• Range is the set of outputs
• Often restricted by context or convenience