Question

Which relations are functions?

A. Relations where each input has exactly one unique output.
B. Relations where each input has multiple outputs.
C. Relations with no specific input-output pattern.
D. Relations with only one input and one output.

Answer 1

In mathematics, a function is a relation where each input has exactly one unique output, which aligns with Option A. Options B and C are incorrect as they allow for multiple outputs for a single input or no specific pattern. While Option D could technically describe a function, it is too narrowly defined.

Step-by-step explanation:

A function in mathematics describes a specific type of relationship between sets of numbers. For a relation to be classified as a function, each input (or 'x' value) within the domain must correspond to exactly one output (or 'y' value) within the range. This concept can be compared to a real-world scenario where, for example, each student has a unique ID number.

Based on the options provided, the correct answer is:

• Relations where each input has exactly one unique output are functions (Option A).

Options B and C do not describe functions because in these cases, an input can have multiple outputs or no specific pattern, both of which violate the definition of a function. Option D would indeed describe a function, but it's narrowly defined and not inclusive of all functions, as functions can have more than one input/output pair.