The graph shows a rational function with vertical asymptotes at $x = -2$ and $x = 4$. The function has a hyperbola-like behavior with these asymptotes, indicating that the function likely involves terms of the form $\frac{1}{x - a}$, where $a$ corresponds to the location of the asymptotes.

The vertical asymptotes are at $x = -2$ and $x = 4$, suggesting that the denominator of the rational function should include the factors $(x + 2)$ and $(x - 4)$. The overall structure of the function seems to follow a reciprocal relationship, and the graph looks like the following function:

$y = \frac{1}{(x + 2)(x - 4)}$

This function will have vertical asymptotes where the denominator is zero, at $x = -2$ and $x = 4$, consistent with the graph.

Would you like further details or explanations on this? Here are some related questions to explore this concept further:

1. How do vertical asymptotes affect the shape of a graph?
2. What happens to the function as $x$ approaches the vertical asymptotes?
3. How can you determine the horizontal asymptote of a rational function?
4. Can you manipulate the numerator to change the graph without changing the asymptotes?
5. How would adding constants to the function affect the graph?

Tip: Always check the locations of asymptotes and intercepts to identify the form of a rational function.