Which statement about a function is true?

Which statement about a function is true?

• A. A function may not have any output for some inputs.
• B. A function assigns more than one output to each input.
• C. A function is defined only for a finite domain.
• D. A function assigns exactly one output to each input.

Answer: (D)

The essential idea is that a function is a rule that assigns one and only one output to every input in its domain. That single-output requirement is what makes something a function rather than just a general relation. If an input had no output, or if the rule could give multiple outputs for the same input, it wouldn’t be a function. Also, the domain of a function isn’t limited to be finite; it can be finite or infinite. For example, f(x) = x^2 with domain all real numbers gives exactly one output for each input (like f(2) = 4 and f(-3) = 9).

The essential idea is that a function is a rule that assigns one and only one output to every input in its domain. That single-output requirement is what makes something a function rather than just a general relation. If an input had no output, or if the rule could give multiple outputs for the same input, it wouldn’t be a function. Also, the domain of a function isn’t limited to be finite; it can be finite or infinite. For example, f(x) = x^2 with domain all real numbers gives exactly one output for each input (like f(2) = 4 and f(-3) = 9).