Describing Transformations of Rational Functions

First, we can rewrite $g(x)$ by moving the numerator in front of the fraction. In that way, we can see that the fraction is the parent function $f(x).$ $$g(x)=\frac{5}{x}\iff g(x)=5\cdot \frac{1}{x}$$ Let's start by recalling possible transformations of the parent function $f(x)=\frac{1}{x}.$

Now, let's consider the given function. $$\begin{array}{c}g(x)=5\cdot \frac{1}{x}\end{array}$$ We can see that $a=5.$ Therefore, the graph of $g(x)$ is a vertical stretch of the graph of $f(x)$ by a factor of $5.$