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Describing Transformations of Rational Functions

Describing Transformations of Rational Functions 1.13 - Solution

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

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

Now, let's consider the given function. g(x)=10.1xg(x)=10.1x\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 b=10.1=10.\textcolor{magenta}{b}=\frac{1}{0.1}=\textcolor{magenta}{10}. Therefore, the graph of g(x)g(x) is a horizontal stretch of the graph of f(x)f(x) by a factor of 10.\textcolor{magenta}{10}.