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To determine the equation of this rational function based on the graph, we can observe a few key features:

1. **Vertical Asymptote**: The graph has a vertical asymptote at \( x = -5 \), indicating the function has a factor in the denominator that makes it undefined at \( x = -5 \).

2. **Horizontal Asymptote**: The graph has a horizontal asymptote at \( y = 0 \), suggesting the degree of the numerator is less than or equal to the degree of the denominator.

3. **Behavior of the Function**: The function approaches positive and negative infinity as \( x \) approaches \( -5 \), indicating a simple pole at \( x = -5 \).

A rational function with these properties can be represented as:
\[
f(x) = \frac{k}{x + 5}
\]
where \( k \) is a constant that would affect the steepness or direction of the function. By adjusting \( k \) to match the given graph's specific growth rate or decline, we could finalize the function's form. 

Would you like further details on how to determine \( k \), or have any questions about rational function properties?

Here are some questions to consider:

1. What does the constant \( k \) represent in a rational function?
2. How would the function change if the asymptote was at \( x = 3 \) instead of \( x = -5 \)?
3. How do you determine the horizontal asymptote of a rational function?
4. What is the impact of having a higher degree in the numerator versus the denominator?
5. How can you find the domain of a rational function like this one?

**Tip**: The vertical asymptote in a rational function reveals the values for which the function is undefined due to the denominator becoming zero.

Find the equation of the rational function, whose graph is shown below.

Learn how to find the equation of a rational function from its graph, focusing on vertical and horizontal asymptotes. This problem demonstrates key concepts in rational functions, including asymptote behavior and function form.

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