Null Function/Examples/Example 3

Example of Null Function
Let $f: \R \to \R$ be the real function defined as:
 * $\forall x \in \R: \map f x = \begin {cases} 1 & : t = 1 \le t \le 2 \\ 0 & : \text {otherwise} \end {cases}$

Then $f$ is not a null function.

Proof
Let $x > 2$.

Hence the result by definition of null function.