What is a function rule?

A function rule, often simply called a "rule," is a mathematical expression or a set of instructions that defines how one variable (the input) relates to another variable (the output) in a mathematical function. In other words, it describes the relationship between the independent variable (often denoted as "x") and the dependent variable (often denoted as "y") in a function.

A function rule typically takes the form of an equation or formula and can include mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more. The function rule specifies how the input values are transformed into output values. For example, in the function rule "y = 2x + 3," the input (x) is multiplied by 2, and then 3 is added to the result to obtain the output (y).

Function rules are fundamental in mathematics and are used to describe relationships between variables in various contexts, such as linear functions, quadratic functions, trigonometric functions, exponential functions, and many others. They are a key concept in algebra and are essential for solving equations, graphing functions, and analyzing mathematical relationships.