What is a function rule in algebra?

A function rule in algebra is best described as an algebraic expression that defines a function. This means that the function rule provides a clear relationship between the input (often represented as x) and the output (often represented as f(x)). Through this expression, one can determine what output to expect from a given input, establishing a specific rule for how to transform the input into the output.

For example, in the function rule f(x) = 2x + 3, the function defines how any input x is mapped to its corresponding output by multiplying x by 2 and then adding 3. This encapsulates the essence of what a function is: a relationship between inputs and outputs, governed by a specific rule or expression.

This understanding underscores the fundamental concept of functions in algebra, where the focus lies on how variables interact through defined operations. Other choices may highlight related ideas but do not accurately capture the primary definition of a function rule as it pertains to algebraic functions.