Definition
Domain of a function
The domain of a function is the set of input values the function is allowed to use.
What it means
Think about the function’s input door. The domain is the complete list or rule for what may go in. For f(x) = 10 ÷ x, zero is kept out because division by zero is not defined. In a story, the context can also narrow the inputs—for example, a number of tickets cannot be negative.
Remember it
Domain answers one question: Which inputs are allowed?
Example
Let f(n) = 2n + 1 for n in {0, 1, 2, 3}. The domain is {0, 1, 2, 3}. The outputs 1, 3, 5, and 7 are not the domain.
Watch for
The domain is not the set of outputs; outputs belong to the range of the function.
Common mix-up
The everyday word domain can mean a field or subject. This term owns the function-input sense.
Exact meaning
The domain of a function is the set of all inputs for which the function is defined. It may be listed, stated by a rule, or limited by the formula or by the real-world context.