It looks like you're working on a problem related to horizontal and vertical asymptotes. Based on the information you've submitted, the horizontal asymptote appears to be correct with a value of 4. However, the vertical asymptote answer ("DNE") seems to be incorrect.

The function $f(x)$ you provided has the following limits:

• $\lim_{x \to \infty} f(x) = \infty$
• $\lim_{x \to -\infty} f(x) = 4$
• $\lim_{x \to \infty} f(x) = 4$
• $\lim_{x \to -\infty} f(x) = -\infty$

Based on these limits, the vertical asymptote would typically be determined by observing the behavior as $x$ approaches a particular value, such as where the function tends toward infinity or negative infinity.

Can you confirm the type of function $f(x)$ you're working with? It would be helpful for identifying whether there is a specific point where the function behaves as described, especially for the vertical asymptote.

Let me know if you'd like further details or have any questions!

Here are some related questions to consider:

1. What type of function typically has a vertical asymptote at a certain value of $x$?
2. How can you determine the vertical asymptote of rational functions?
3. What do the limits at $x \to \infty$ and $x \to -\infty$ tell you about the horizontal asymptote?
4. How does the behavior of a function at infinity help determine the horizontal asymptote?
5. Could there be a discontinuity in the function that causes the vertical asymptote?

Tip: Always examine the function's form first. For rational functions, vertical asymptotes typically occur where the denominator equals zero and the numerator does not cancel it out.