Which of the following best describes a function in the context of business calculus?

• A. A rule that assigns each input exactly one output.
• B. A table listing possible outputs for any input.
• C. A process that randomly matches inputs to multiple outputs.
• D. A graph that shows only the outputs of a business process.

Answer: (A)

Verified step by step guidance

1. Understand the definition of a function: In mathematics, a function is a rule or relationship that assigns each input (from the domain) exactly one output (in the range). This is a key concept in calculus and is foundational for business applications.
2. Eliminate incorrect options: A table listing possible outputs for any input does not necessarily define a function because it may not ensure that each input has exactly one output.
3. Eliminate incorrect options: A process that randomly matches inputs to multiple outputs violates the definition of a function, as a function must assign exactly one output to each input.
4. Eliminate incorrect options: A graph that shows only the outputs of a business process does not provide the necessary relationship between inputs and outputs, which is essential for defining a function.
5. Conclude: The correct description of a function is 'A rule that assigns each input exactly one output,' as it aligns with the mathematical definition of a function.