When the graph of the function $y=\text{f}(x)$, defined on the real numbers, is reflected in the $y$-axis and then translated by $2$ units in the negative $x$-direction, the result is the graph of the function $y=\text{g}(x)$.

When the graph of the same function $y=\text{f}(x)$ is translated by $2$ units in the negative $x$-direction and then reflected in the $y$-axis, the result is the graph of the function $y=\text{h}(x)$.

Which one of the following conditions on $y=\text{f}(x)$ is necessary and sufficient for the functions $\text{g}(x)$ and $\text{h}(x)$ to be identical?