Describing Transformations of Rational Functions

Let's start by recalling possible transformations of the parent function $f(x)=\frac{1}{x}.$

Now, let's consider the given function. $\begin{gathered} g(x)=\dfrac{1}{0.1x} \quad \Leftrightarrow \quad g(x)=\dfrac{1}{\textcolor{magenta}{0.1}x} \end{gathered}$ We can see that $\textcolor{magenta}{b}=\frac{1}{0.1}=\textcolor{magenta}{10}.$ Therefore, the graph of $g(x)$ is a horizontal stretch of the graph of $f(x)$ by a factor of $\textcolor{magenta}{10}.$