What is function rule?

A function rule is a mathematical equation that relates two variables, typically denoted by x and y. It represents a specific relationship between the input value (x) and the output value (y) of a function.

The function rule can be written in various forms, such as:

1. Algebraic expression: An equation that represents the relationship between x and y using mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Examples include y = 2x + 3 or y = x^2.

2. Table: A set of input-output pairs listed in a table format, where each input value corresponds to its corresponding output value. For example:

   x | y

   1 | 4 2 | 7 3 | 10

   In this table, the function rule can be written as y = 3x + 1, which means the output (y) is obtained by multiplying the input (x) by 3 and adding 1.

3. Graph: A graphical representation of the relationship between x and y on a coordinate plane. The function rule is often represented as a line or curve that passes through various points. For example, a linear function rule y = mx + b represents a straight line, where m is the slope and b is the y-intercept.

Function rules are used to describe and analyze relationships in various fields of study, including mathematics, physics, economics, and computer science. They help in modeling and predicting outcomes based on given input values. By manipulating the function rule using algebraic operations, one can solve equations, find unknown values, and make predictions or inferences.