Which of the following best describes a function in mathematics?

• A. A set of ordered pairs with no restrictions.
• B. A relation where each input has exactly one output.
• C. A relation where each output has exactly one input.
• D. A process that assigns multiple outputs to a single input.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the definition of a function in mathematics. A function is a relation where each input (from the domain) is assigned to exactly one output (in the range). This means no input can have more than one output.
2. Step 2: Analyze the first option: 'A set of ordered pairs with no restrictions.' This is incorrect because a function must follow the rule that each input has exactly one output, which is a restriction.
3. Step 3: Analyze the second option: 'A relation where each input has exactly one output.' This is correct because it aligns with the definition of a function in mathematics.
4. Step 4: Analyze the third option: 'A relation where each output has exactly one input.' This is incorrect because a function does not require that each output be associated with only one input. Multiple inputs can share the same output.
5. Step 5: Analyze the fourth option: 'A process that assigns multiple outputs to a single input.' This is incorrect because a function cannot assign more than one output to a single input, as it violates the definition of a function.