
Define an identity function and draw its graph, also find its domain and range.
Answer
432k+ views
Hint:We are given a question asking us to define an identity function and then graph it and further, find the function’s domain and range. An identity function is one that has each of its elements in the domain and has an image of itself in the range. The function for the same can be defined as, we have, for all values of x belonging to R, , is the identity function on R. We will graph the function, which will give us a straight line passing through origin. The domain and range can clearly be obtained from the functions definition. Hence, we will have the required function.
Complete step by step answer:
According to the given question, we are asked to define an identity function and draw the graph of the respective function and then we have to mention the function’s domain and range.
An identity function is one that has each of its elements in the domain and has an image of itself as the range.
The function can be defined as,
, for all values of
That is,
So, we have the function as,
We will draw the graph of this function and for that, we will plot some points and we have,
That is, for any value of ‘x’, the function has same value.
We get the graph as,
We can see that the graph is a straight line passing through the origin.
And it is defined from the set of real numbers. So, we have the domain and the range as the set of all real numbers, that is,
Domain of the function = R
Range of the function = R
Note: The identity function should be confused with the function having 1 in the range. Also, to graph any function, always find the coordinates first and not do it directly, so as to reduce the risk of getting the graph wrong. The domain refers to the values of the ‘x’ and range refers to the values of or ‘y’.
Complete step by step answer:
According to the given question, we are asked to define an identity function and draw the graph of the respective function and then we have to mention the function’s domain and range.
An identity function is one that has each of its elements in the domain and has an image of itself as the range.
The function can be defined as,
That is,
So, we have the function as,
We will draw the graph of this function and for that, we will plot some points and we have,
-2 | -1 | 0 | 1 | 2 | |
-2 | -1 | 0 | 1 | 2 |
That is, for any value of ‘x’, the function has same value.
We get the graph as,

We can see that the graph is a straight line passing through the origin.
And it is defined from the set of real numbers. So, we have the domain and the range as the set of all real numbers, that is,
Domain of the function = R
Range of the function = R
Note: The identity function should be confused with the function having 1 in the range. Also, to graph any function, always find the coordinates first and not do it directly, so as to reduce the risk of getting the graph wrong. The domain refers to the values of the ‘x’ and range refers to the values of
Recently Updated Pages
Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Which one of the following is a true fish A Jellyfish class 12 biology CBSE

a Tabulate the differences in the characteristics of class 12 chemistry CBSE

Why is the cell called the structural and functional class 12 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Write the difference between solid liquid and gas class 12 chemistry CBSE

What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?
