What is an adequate counter example to disprove that if $A$ is open $f(A)$ is also open?

Question

What is an adequate counter example to disprove that if $A$ is open $f(A)$ is also open?

$$A \subseteq \mathbb{R} \rightarrow \mathbb{R}.$$

Answer 1

Consider the function $f(x) = 0$. For any non-empty $A \subset \mathbb{R}$,

$$f(A) = \{0\}$$

Which is not open.

$\textit{Edited thanks to clarifying comments.}$