First, we will try to understand this topic with a general example. Any person knows about shopping and has done it. You must have encountered price tag stands with some materials in them. If you haven’t seen such stands, then please consider the below picture as an example. In this picture, everything which is placed under that stand is a set price; moreover you can be lucky enough to find a sale. Now, in this case, a relationship can be established between the items which are under the stand and their prices. This is exactly an example of Constant function.
Here “a” is a number and it is not dependent on x. You all must be wondering how a Constant Function will look like in a graph. Have you ever seen a horizontal line? That is the graphical representation of Constant Function. So in the graphical representation of a Constant Function a horizontal line is included that means a line with slope 0. To elaborate the graphical representation, we can say that in a constant function where y = b , it means that everywhere a Constant Function has a y value and there would be no change in the value of y. So the graph stays constant and would form the horizontal line.
The constant function can be understood by simple understanding. Now ask yourself: How can you differentiate between the Constant Function and not a Constant Function? Or can you have different outputs for the different inputs? If you are having different outputs for the different inputs, you don’t have Constant Function. If you are having the same output regardless of the different values of input then only you have Constant Function. We will understand this Non-Constant Function through a example.
If someone wants to write a Constant Function formally, it can be written as f (x): R→R and it has the form as f (x) = c. Generally, a Constant Function is written as y (x) = c or it can be written as y = c
• Idempotent is a term which is used when every constant function whose co-domain and domain are the same.
Everyone knows that functions are widespread and can be seen in mathematics on a daily basis. You must have encountered various kinds of functions in mathematics – such as odd and even functions, surjective function, the identity function, constant function, injective function, bijective function etc. But now we will be focussing on the Identity Function.
Properties of any function are the main part of that function so there is a need to describe them in details. Now let’s discuss the properties of Identity Function in brief: