What is a function rule?

A function rule in mathematics is a relationship between two sets of numbers where each input has exactly one output. It is a mathematical expression that defines how one quantity depends on another. Function rules can be represented in a variety of ways, such as algebraic equations, tables, graphs, or verbal descriptions.

For example, the function rule f(x) = 2x + 3 represents a linear function where the output is equal to two times the input plus three. This rule can be used to find the output value (y) for any given input value (x).

Function rules can also be used to model real-world situations, such as calculating the cost of an item based on the number of items purchased or determining the height of a projectile based on time and initial velocity.

Overall, function rules are important in mathematics because they help us understand and analyze relationships between quantities and make predictions based on those relationships.