Question

the asymptote of the function is \\(\boldsymbol{x = 2}\\)\\(\boldsymbol{x = -2}\\)\\(\boldsymbol{x = 3}\\)\\(\boldsymbol{x = -3}\\) \\(\boldsymbol{\downarrow}\\) . for very high \\(x\\)-values, \\(y\\) \\(\boldsymbol{\square}\\)

Explanation:

Step1: Identify vertical asymptote

The graph approaches the vertical line $x=3$ but never touches it, so this is the vertical asymptote.

Step2: Analyze high x-values trend

As $x$ increases to very large values, the graph moves upward, meaning $y$ increases toward positive infinity.

Answer:

The asymptote of the function is $\boldsymbol{x=3}$. For very high x-values, $\boldsymbol{y \text{ approaches positive infinity (increases without bound)}}$