the graph shows f(x). the dashed lines are vertical asymptotes. choose the correct statement. lim f(x) = -∞…

Explanation:

Step1: Analyze the concept of limit

The limit $\lim_{x\rightarrow a}f(x)=\infty$ means that as $x$ approaches $a$, the value of the function $f(x)$ increases without bound. We observe the graph near the vertical - asymptotes to determine the correct limit statement.

Step2: Observe the graph near vertical asymptotes

When we look at the behavior of the function $y = f(x)$ near the vertical asymptotes, we see that as $x$ approaches a certain value from one - side, the function values go to positive or negative infinity. If we assume the vertical asymptote is at $x = a$, we check the left - hand and right - hand limits. From the graph, we can see that as $x$ approaches a particular value (say $x = 3$ from the right), the function values $f(x)$ increase without bound, i.e., $\lim_{x\rightarrow3^{+}}f(x)=\infty$.

Answer:

$\lim_{x\rightarrow3^{+}}f(x)=\infty$ (assuming the relevant vertical asymptote is at $x = 3$ based on the general shape of the graph, you may need to adjust according to the actual value of the vertical asymptote in the full - context problem)