Question

1. use the graph of f(x) to find the vertical asymptote(s). use limit notation: zero(s): x = 6 vert. asymp.(s): x = 0

Explanation:

Step1: Identify vertical asymptotes

Vertical asymptotes occur where the function approaches infinity or negative - infinity. From the graph, we can see that the function approaches infinity or negative - infinity at \(x = 0\).

Step2: Write in limit notation

The limit notation for the vertical asymptote \(x = 0\) is \(\lim_{x
ightarrow0^{-}}f(x)=\pm\infty\) and \(\lim_{x
ightarrow0^{+}}f(x)=\pm\infty\) (the sign of infinity depends on the behavior of the function on either side of \(x = 0\)). In general, for a vertical asymptote \(x = a\), we write \(\lim_{x
ightarrow a^{-}}f(x)=\pm\infty\) and \(\lim_{x
ightarrow a^{+}}f(x)=\pm\infty\). Here \(a = 0\).

Answer:

Vertical asymptote: \(x = 0\), Limit notation: \(\lim_{x
ightarrow0^{-}}f(x)=\pm\infty,\lim_{x
ightarrow0^{+}}f(x)=\pm\infty\)