What is a function?

What is a function?

• A. A single number.
• B. A line with no slope.
• C. Relationship between two sets of data.
• D. A ratio expressed as a fraction.

Answer: (C)

A function is a rule that assigns exactly one output to each input. You can picture it as a relationship between two sets of data: inputs (domain) and outputs (range) connected by a fixed rule. A function can be shown in a formula, a graph, or a table, and on a graph it passes the vertical line test—no vertical line should hit the graph more than once. Choosing a description that emphasizes mapping inputs to outputs best captures the idea. A single number isn’t a rule that covers all inputs. A line with no slope describes a horizontal line, which can be a function but isn’t the general definition. A ratio expressed as a fraction is just a number, not a mapping from inputs to outputs.

A function is a rule that assigns exactly one output to each input. You can picture it as a relationship between two sets of data: inputs (domain) and outputs (range) connected by a fixed rule. A function can be shown in a formula, a graph, or a table, and on a graph it passes the vertical line test—no vertical line should hit the graph more than once.

Choosing a description that emphasizes mapping inputs to outputs best captures the idea. A single number isn’t a rule that covers all inputs. A line with no slope describes a horizontal line, which can be a function but isn’t the general definition. A ratio expressed as a fraction is just a number, not a mapping from inputs to outputs.