Question

refer to the graph of y = f(x) to the right to describe the behavior at the limit. lim f(x). use -∞ and ∞ where appropriate. x→ - 3 select the correct choice below and fill in any answer boxes in your choice. a. lim f(x)= x→ - 3 b. the limit does not exist and is neither -∞ nor ∞.

Explanation:

Step1: Analyze left - hand limit

As $x$ approaches $- 3$ from the left side ($x\to - 3^{-}$), observe the graph. The function values $y = f(x)$ approach $-\infty$.

Step2: Analyze right - hand limit

As $x$ approaches $- 3$ from the right side ($x\to - 3^{+}$), observe the graph. The function values $y = f(x)$ approach $\infty$.

Step3: Determine overall limit

Since the left - hand limit $\lim_{x\to - 3^{-}}f(x)=-\infty$ and the right - hand limit $\lim_{x\to - 3^{+}}f(x)=\infty$, the two - sided limit $\lim_{x\to - 3}f(x)$ does not exist and is neither $-\infty$ nor $\infty$.

Answer:

B. The limit does not exist and is neither $-\infty$ nor $\infty$.