Question

How do you find the function rule?

Answer 1

Hint: A function rule usually consists of common calculations or formulas with help of the input part and gets results in the terms of output.
Functions consist of three components:
1. Input parameters
2. Output parameters
3. Operational formula
Use this information to find function rules for any set of given sequenced data.

Complete step by step answer:
In order to find function rules, let us first know what a function rule is?
In the form of an equation, a function rule is the relationship between the dependent and independent variables. The function rule of a particular function describes how the value of the dependent variable, say y, can be calculated in terms of the independent variable, say x. A function rule is, in simple words, known as the process that changes the input value to the output.

Now coming to the question, we can find function rules from a set of data or from a particular graph. Let us understand this with an example,
We are going to gift chocolates to children, the below table shows relation between number of chocolates and its price

Number of chocolates	$1$	$2$	$3$	$4$	$5$	$6$
Price (in Rs)	$10$	$20$	$30$	$40$	$50$	$60$

Now, the price is given for particular amount of chocolates, we will generalize and write its function rule,
Let the number of chocolates be $x$ and its price be Rs $y$
According to table,
$$\begin{gathered} 1\text{chocolate}=10\text{Rs} \\ x\text{chocolates}=x\times 10\text{Rs}=y \\ \Rightarrow y=10x \end{gathered}$$
So $y=10x$ is the function rule for this example.

Note: It is not necessary that every group of data must have a function rule, function rule can be written only for an organized set of data that means data which follow a particular sequence not any random set of data can have function rule.