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

• A. A table that lists all possible input and output pairs without any specific rule.
• B. A relationship that assigns exactly one output value to each input value from a given set.
• C. A calculation that only uses constant values and does not depend on any input.
• D. A process that randomly matches inputs to multiple outputs.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the definition of a function in the context of calculus. A function is a relationship where each input (from the domain) is assigned exactly one output (from the range). This is a key concept in calculus and is foundational for understanding how variables interact in mathematical models.
2. Step 2: Analyze the options provided in the problem. Eliminate any options that do not align with the definition of a function. For example, a table listing all possible input-output pairs without a specific rule does not meet the criteria of a function because it lacks a defined relationship.
3. Step 3: Consider the option that describes a calculation using only constant values. This does not depend on any input and therefore does not represent a function, as a function requires a relationship between inputs and outputs.
4. Step 4: Evaluate the option describing a process that randomly matches inputs to multiple outputs. This violates the definition of a function, as a function must assign exactly one output to each input.
5. Step 5: Conclude that the correct answer is the option stating 'A relationship that assigns exactly one output value to each input value from a given set,' as this aligns with the formal definition of a function in calculus.