One graph with three different types of asymptotes

Question

This graph is what I came up with while searching for one that had three different types of asymptotes, horizontal, vertical, and oblique.$f(x)=\sqrt{x^2+\frac{1}{x^2}}+x$

Can you provide other functions with three asymptotes? Please share your ideas.

Answer 1

Another example is $\displaystyle f(x) = \frac{x-e^x}{1-e^x}$.