Let's analyze the characteristics given for the function $y = f(x)$:

1. Limit as $x \to \infty$:
   $\lim_{x \to \infty} f(x) = 3$
   This implies that as $x$ approaches infinity, the function $f(x)$ approaches the horizontal asymptote $y = 3$.

2. Limit as $x \to -\infty$:
   $\lim_{x \to -\infty} f(x) = -5$
   This suggests that as $x$ approaches negative infinity, $f(x)$ approaches the horizontal asymptote $y = -5$.

3. Limit as $x \to -1^{-}$:
   $\lim_{x \to -1^{-}} f(x) = \infty$
   This means that as $x$ approaches $-1$ from the left side, $f(x)$ goes to positive infinity. This indicates a vertical asymptote at $x = -1$, where $f(x) \to \infty$ from the left.

4. Limit as $x \to -1^{+}$:
   $\lim_{x \to -1^{+}} f(x) = -\infty$
   As $x$ approaches $-1$ from the right, $f(x)$ goes to negative infinity. This again confirms a vertical asymptote at $x = -1$, where $f(x) \to -\infty$ from the right.

Summary of Key Features:

• Horizontal asymptote at $y = 3$ as $x \to \infty$.
• Horizontal asymptote at $y = -5$ as $x \to -\infty$.
• Vertical asymptote at $x = -1$, with $f(x) \to \infty$ from the left and $f(x) \to -\infty$ from the right.

To identify which graph matches these features, look for:

1. A horizontal line approaching $y = 3$ on the far right.
2. A horizontal line approaching $y = -5$ on the far left.
3. A vertical line at $x = -1$ where the graph goes up to $+\infty$ on the left side and down to $-\infty$ on the right side.

Would you like more details or have any further questions?

Here are 5 related questions:

1. What other types of asymptotes can a function have?
2. How does the limit behavior of $f(x)$ affect the overall shape of the graph?
3. Can a function have multiple vertical asymptotes? If so, how do we identify them?
4. How would the function behave if the limits at infinity were not constants?
5. How does a vertical asymptote differ from a hole in a function's graph?

Tip: When analyzing graphs of functions, always pay attention to both horizontal and vertical asymptotes to understand long-term behavior and potential discontinuities.