Answer
$d(x)=x-3$
Work Step by Step
The $\textit{signed distance}$ $d(x)$ from $a$ to $b$ is $b-a$. Therefore the signed distance from $3$ to any number $x$ is:
$$d(x)=x-3.$$
Since $x$ can be any number, the domain of the function is the set of all real numbers:
$$\text{Domain}=(-\infty,\infty)$$
The range consists of all real numbers:
$$\text{Range}=(-\infty,\infty)$$
As the graph is unbroken, the function is continuous.
