Question

Define an identity function and draw its graph, also find its domain and range.

Answer 1

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, \[f:R\to R\] we have, \[f(x)=x\] for all values of x belonging to R, \[x\in R\], 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,
\[f:R\to R\], \[f(x)=x\] for all values of \[x\in R\]
That is, \[y=x\]
So, we have the function as, \[y=f(x)=x\]
We will draw the graph of this function and for that, we will plot some points and we have,

\[x\]	-2	-1	0	1	2
\[f(x)\]	-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 \[f(x)\] or ‘y’.