Give an example of a set $S$ whose support function is not continuous on $R^n$.

Question

Let $A \subseteq \mathbb{R}^n$.

The support function of set $A$ is defined as the following

$$ S_A(x)=\sup_{y \in A} x^Ty $$ where $x \in \mathbb{R}^n$.

Notice that when $A$ is bounded the function is continuous.

Give an example of a set except $S\neq \mathbb{R}^n$ whose support function is not continuous on $\mathbb{R}^n$.