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# What is a function rule?

Last updated date: 20th Sep 2024
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Hint: A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by$f\left( x \right)$ where x is the input. The general representation of a function is $y = f\left( x \right)$.

Complete step by step solution:
A function rule is the relationship between the dependent and independent variables in the form of an equation. The function rule of a specific function, explains how to determine the value of the dependent variable say y, in terms of the independent variable say x. In simple words, a function rule is defined as the process that changes the input value to output.
Let us explain the function rule with an example:
Ex. Write a function rule for the following table given:

 Input 1 2 3 4 5 Output 5 6 7 8 9

output is obtained when four are added to input. Hence,
Let I be Input
Let O be the Output
Now let us write the equation by obtained data as
$O = 4 + I$
Hence, in this way function rules are applied.

Note: A user defined function contains common calculations or functionality that can be broken out into distinct and logical pieces. A function can be used repeatedly by calling the function. Functions define what values need to be input in order for the calculation to run correctly. Functions also define what is the output for the given input of the data.