the graph of the function has a vertical asymptote of x = \nthe graph of the function has a horizontal…

Explanation:

Step1: Recall vertical - asymptote concept

For a rational function $y = \frac{1}{x}$, the denominator cannot be zero. When $x = 0$, the function is undefined. So the vertical asymptote is $x = 0$.

Step2: Recall horizontal - asymptote concept

As $x\rightarrow\pm\infty$, we consider the limit of $y=\frac{1}{x}$. $\lim_{x\rightarrow\pm\infty}\frac{1}{x}=0$. So the horizontal asymptote is $y = 0$.

Answer:

The graph of the function has a vertical asymptote of $x = 0$. The graph of the function has a horizontal asymptote of $y = 0$.