To determine the equation for the function graphed in the image, let's analyze the key features visible:

1. Vertical Asymptotes: The graph has vertical asymptotes at $x = -3$ and $x = 2$. This suggests that the function likely has factors in the denominator that cause the function to approach infinity as $x$ approaches these values.

2. Behavior of the Function: The graph resembles a rational function with vertical asymptotes and undefined points. Given the asymptotes at $x = -3$ and $x = 2$, the denominator of the function could include factors like $(x + 3)(x - 2)$.

3. Horizontal Asymptote: The function seems to level off towards a horizontal asymptote at $y = 0$ as $x$ moves to positive and negative infinity, indicating that the degree of the numerator is lower than or equal to the degree of the denominator.

A basic function that meets these conditions would be: $y = \frac{1}{(x + 3)(x - 2)}$

This form has vertical asymptotes at $x = -3$ and $x = 2$, as well as a horizontal asymptote at $y = 0$.

Final Answer:

$y = \frac{1}{(x + 3)(x - 2)}$

Would you like a deeper explanation of this solution or have any other questions?

Here are some related questions to expand your understanding:

1. What would happen if the numerator had a term $x^2$ instead of a constant?
2. How do vertical asymptotes affect the shape of a graph?
3. What conditions lead to a horizontal asymptote at $y = 0$?
4. Can a rational function have more than two vertical asymptotes?
5. How would the equation change if there were a horizontal asymptote at $y = 2$?

Tip: For rational functions, vertical asymptotes occur where the denominator equals zero (and the numerator doesn’t also go to zero at those points).