Linear functions

Let \(A\) and \(B\) be subsets of the real line. A function \(L\) which is such that each \(x \in A\) is assigned to the real number \(ax+b \in B\), where \(a,b\) are constants is called a linear function.

In particular, when \(a = 0\), then this becomes the constant function that sends every element \(x \in A\) to the constant \(b \in B\) . Thus, every constant function is a special instance of a linear function.