Chapter 6 Elementary Functions

Section 6.2 Linear Functions and Polynomials

6.2.2 Constant Functions and the Identity

so-called constant functions assign to every number in the domain exactly the same constant number in the target set , e.g. the constant number 2, in the following way:

f:  { x2.

Here, we then have f(x)=2 for all x. Hence, the range of this function f consists only of the set Wf ={2}.
The identity function on is the function that assigns each real number to itself. This is written as follows:

Id:  { xx.

Here, we then have Id(x)=x for all x. Hence, the range of Id is the set of real numbers ( WId =). Furthermore, the identity function is (obviously) a strictly increasing function.