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Write an equation for the function graphed y = 

The graph depicts a function with vertical asymptotes at \(x = -3\) and \(x = 4\). The behavior of the function suggests it is a rational function with these vertical asymptotes.

Considering the vertical asymptotes at \(x = -3\) and \(x = 4\), the function can be written in the form:
\[ y = \frac{A}{(x+3)(x-4)} \]

To determine \(A\), we need more specific points from the graph or additional information, but without specific points, we assume a simple rational function. Therefore, one possible equation for the function is:
\[ y = \frac{1}{(x+3)(x-4)} \]

If you have any specific points from the graph, we could refine the function further. Would you like details or have any questions about this function? 

Here are some related questions you might find useful:

1. What are the vertical and horizontal asymptotes of a rational function?
2. How do you determine the vertical asymptotes of a rational function?
3. What is the significance of the numerator in a rational function?
4. How do you find the horizontal asymptote of a rational function?
5. What is the difference between removable and non-removable discontinuities?
6. How can you determine the x-intercepts of a rational function?
7. What role do the degrees of the numerator and denominator play in the graph of a rational function?
8. How do you find the oblique asymptote of a rational function?

**Tip:** When analyzing rational functions, always look for vertical asymptotes by setting the denominator equal to zero and solving for \(x\). This will help you understand where the function has undefined points.

Explore the concept of rational functions and vertical asymptotes with a detailed explanation. Learn how to identify and solve problems involving rational functions, specifically addressing vertical asymptotes at x = -3 and x = 4. Suitable for Grades 10-12.

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