Identity Function

Let $f: A \to A$ be a function. If every element in the domain maps directly to itself, then this function is called the identity function.

That is, for all $x \in A$, $f(x) = x$. The identity function is typically denoted by $I$.

\[
f: A \to A, \quad f(x) = x
\]

\[
f(1) = 1, \quad f(2) = 2, \quad f(3) = 3, \quad f(4) = 4
\]

The graph of the identity function $f: \mathbb{R} \to \mathbb{R}, \quad f(x) = x$ is represented as follows:

is a line passing through the origin at a $45^\circ$ angle, also known as the first bisector.