An example for a function which is a relation, (Domain-R, Codomain-R) is:
This question has multiple correct options
A. $y = x$
B. $y = x - 1$
C. $y = {x^2}$
D. None of these



Last updated date: 22nd Mar 2023
•
Total views: 308.4k
•
Views today: 5.88k
Answer
308.4k+ views
Hint- Here, we will proceed by analysing the graph of each function and then drawing a vertical line.
Every function is a relation when each input has only one output. It means that for a particular value of $x$, there should be only one value of $y$ corresponding to that value of $x$.
This can be checked by drawing a vertical line in the graph of the function and if this vertical line cuts at exactly one point on the curve of the function, then that function is a relation whereas if this vertical line cuts at more than one point on the curve of the function, then this function is not a relation.
Now, figures corresponding to each function given in the options are drawn and then a vertical line is also drawn in each figure. Clearly, in all the figures the vertical line is cutting at exactly one point. Thereby, showing that for one input value there is only one output value.
Hence, all the three given functions i.e., $y = x$, $y = x - 1$ and $y = {x^2}$are examples of relations.
Therefore, options A, B and C are correct.
Note- For function $y = {x^2}$, at $x = 1$ and $x = - 1$ the value of the function is the same which is $y = 1$. Here, corresponding to two inputs there is one same value of output which is possible for a relation because corresponding to each value of input there is only one output.
Every function is a relation when each input has only one output. It means that for a particular value of $x$, there should be only one value of $y$ corresponding to that value of $x$.
This can be checked by drawing a vertical line in the graph of the function and if this vertical line cuts at exactly one point on the curve of the function, then that function is a relation whereas if this vertical line cuts at more than one point on the curve of the function, then this function is not a relation.
Now, figures corresponding to each function given in the options are drawn and then a vertical line is also drawn in each figure. Clearly, in all the figures the vertical line is cutting at exactly one point. Thereby, showing that for one input value there is only one output value.
Hence, all the three given functions i.e., $y = x$, $y = x - 1$ and $y = {x^2}$are examples of relations.
Therefore, options A, B and C are correct.
Note- For function $y = {x^2}$, at $x = 1$ and $x = - 1$ the value of the function is the same which is $y = 1$. Here, corresponding to two inputs there is one same value of output which is possible for a relation because corresponding to each value of input there is only one output.
Recently Updated Pages
Calculate the entropy change involved in the conversion class 11 chemistry JEE_Main

The law formulated by Dr Nernst is A First law of thermodynamics class 11 chemistry JEE_Main

For the reaction at rm0rm0rmC and normal pressure A class 11 chemistry JEE_Main

An engine operating between rm15rm0rm0rmCand rm2rm5rm0rmC class 11 chemistry JEE_Main

For the reaction rm2Clg to rmCrmlrm2rmg the signs of class 11 chemistry JEE_Main

The enthalpy change for the transition of liquid water class 11 chemistry JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Write a letter to the Principal of your school to plead class 10 english CBSE
