Here is the sketch of a function $f(x)$ that satisfies the given conditions. The graph shows:

• $f(0) = 3$.
• As $x \to 2^-$, $f(x) \to \infty$, and as $x \to 2^+$, $f(x) \to -\infty$ (vertical asymptote at $x = 2$).
• As $x \to -\infty$, $f(x) \to -4$, and similarly, as $x \to \infty$, $f(x) \to -4$ (horizontal asymptote at $y = -4$).

Let me know if you have any questions about the function or its graph!

Here are some related questions:

1. How can we identify vertical asymptotes in a function analytically?
2. What role do horizontal asymptotes play in determining the long-term behavior of a function?
3. How can we determine limits of a function as $x$ approaches infinity?
4. How does the value of $f(0) = 3$ affect the overall graph shape?
5. What other types of discontinuities can occur in functions?

Tip: When a limit approaches infinity on one side and negative infinity on the other at the same point, it's a clear sign of a vertical asymptote.