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# Describing Transformations of Rational Functions

## Describing Transformations of Rational Functions 1.13 - Solution

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

Function Transformation of the Graph of $f(x)=\frac{1}{x}$
$g(x)=\dfrac{1}{\textcolor{magenta}{b}\cdot x}$ Horizontal stretch or compression by a factor of $\textcolor{magenta}{b}.$
If $0\lt\textcolor{magenta}{b}\lt 1,$ it is a horizontal stretch.
If $1<\textcolor{magenta}{b},$ it is a horizontal shrink.

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 $\textcolor{magenta}{10}.$