Answer:
The function's behavior close to the vertical asymptote, x = 2 is;
[tex]\lim\limits_{x \to 2^-} f(x) = \infty[/tex] and [tex]\lim\limits_{x \to 2^+} f(x) = -\infty[/tex]
Step-by-step explanation:
From the graph of the function. we have;
1) As 'x' approaches 2 from the left (x → 2⁻), the graph with 'u' shape located in the middle of the three graphs, approaches infinity (arrow pointing up)
2) As 'x' approaches 2 from the right (x → 2⁺), the graph with 'n' shape located at the right side of the three graphs, approaches negative infinity (-∞) (arrow pointing down)
Therefore, the function's behavior close to the vertical asymptote, x = 2 is given as follows;
[tex]\lim\limits_{x \to 2^-} f(x) = \infty[/tex] and [tex]\lim\limits_{x \to 2^+} f(x) = -\infty[/tex]
