Constant functions

Let \(A\) and \(B\) be sets, and \(b_0\) be a given element in \(B\).

Define the function \(k:A \longrightarrow B\) by
\[ k(a) = b_0 \]
for all \(a \in A\).

Then it means that no matter which input element \(a\) you have selected from the domain \(A\), the image of \(a\) under \(k\) is constantly the element \(b_0\). We call such functions constant functions.