In order to find the limit and identify asymptotes, first let's write a table of ordered pairs (x, y) for the given expression:
[tex]\begin{gathered} x=0\rightarrow y=-\frac{1}{10}\\ \\ x=5\rightarrow y=-\frac{1}{5}\\ \\ x=9.9\rightarrow y=-10\\ \\ x=10.1\rightarrow y=10\\ \\ x=15\rightarrow y=\frac{1}{5}\\ \\ x=20\rightarrow y=\frac{1}{10} \end{gathered}[/tex]
Graphing the points and the corresponding curve, we have:
We can see that there is a vertical asymptote at x = 10.
Also, the limit when x tends to 10-, that is, then x tends to 10 from the left, is equal to minus infinity.
