https://file.aiquickdraw.com/mathbot/file/1728277096243jg96pfnv.jpg

The graph you've uploaded resembles a rational function, particularly one with vertical asymptotes at \( x = -2 \) and \( x = 2 \), and possibly a horizontal asymptote at \( y = 0 \). It also appears to have a point where the graph crosses the x-axis, likely suggesting it has a zero at \( x = 0 \).

Given these features, the equation of this function could be expressed as:

\[
y = \frac{a}{(x + 2)(x - 2)}
\]

This form accounts for the vertical asymptotes at \( x = -2 \) and \( x = 2 \). The value of \( a \) could be determined by analyzing the specific behavior at certain points, such as intercepts or other key features visible in the graph.

### Next steps:
- If \( a = -4 \), which fits with the downward shape and range observed, the equation could be refined as:

\[
y = \frac{-4}{(x + 2)(x - 2)}
\]

Would you like more details on how to fine-tune the equation? Feel free to ask for clarification on any part.

### Related Questions:
1. How can we find the constant \( a \) in rational functions using points from the graph?
2. What are vertical asymptotes, and why do they occur in rational functions?
3. What are the x-intercepts, and how are they determined from a rational function's equation?
4. How can we confirm the horizontal asymptote by analyzing the function's end behavior?
5. How does the sign of the constant \( a \) affect the shape of the graph in a rational function?

### Tip:
To identify asymptotes in rational functions, always check the values of \( x \) where the denominator is zero for vertical asymptotes, and analyze the degrees of the polynomial in the numerator and denominator for horizontal asymptotes.

Write an equation for the function graphed below.

Learn how to find the equation of a rational function with vertical asymptotes, as seen in the given graph. Explore how to identify asymptotes and intercepts to form the equation. Suitable for Grades 10-12.

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