Question

How do you find the function rule given \[Input = 20;1;40;4;8;10\] and \[output = 2;40;1;10;5;4\] ?

Answer 1

Hint: Here in this question, we have to find the function where the points are given. In the question we have “write function rule” means the relation of a function where it contains both the function input and output. So, by considering points we calculate the function for the question.

Complete step by step solution:
 By the equation we can determine the values. Likewise, by the inputs and outputs we can find or calculate the function. Here in this question, we have the values of input and output. by using these points we have to determine the function.
There is no common difference between the numbers of the inputs and the outputs also.
So let us multiply the input value and the output value. We write on the table. The table is as shown below:

Input(x)	Output(y)	Product(xy)
20	2	40
1	40	40
40	1	40
4	10	40
8	5	40
10	4	40

So the product is the same.
Therefore we have
 \[ \Rightarrow x.y = 40\]
Let us write the function in terms of y.
so we divide the function by x we have
 \[ \Rightarrow \dfrac{{x.y}}{x} = \dfrac{{40}}{x}\]
On cancelling the term x in the LHS we have
 \[ \Rightarrow y = \dfrac{{40}}{x}\]
Hence we determined the function rule for the question.
So, the correct answer is “$y = \dfrac{{40}}{x}$”.

Note: A function rule describes how to convert an input (x) into an output (y) for a given function. The equation involves the parameter input and output. We can find the value of output by substituting the values of inputs. if we know the points that are coordinate points, we can find the equation by using the equation of line.