https://file.aiquickdraw.com/mathbot/file/1725594889311chyg54f0.jpg

The graph shows a function with a vertical asymptote at \(x = -1\) and a rapid increase to positive and negative infinity near this asymptote, which suggests the presence of a logarithmic function shifted horizontally. Given these characteristics, a likely candidate is a logarithmic function of the form:

\[
y = \ln(x + 1)
\]

This function has the following properties:

- A vertical asymptote at \(x = -1\).
- It rapidly approaches negative infinity as \(x\) approaches \(-1\) from the right.
- It grows slowly after \(x = -1\), similar to the graph.

Therefore, the equation of the function graphed above is:

\[
y = \ln(x + 1)
\]

Would you like more details on this solution, or do you have any questions? 

Here are some related questions you might find interesting:

1. How do you determine the vertical asymptote of a logarithmic function?
2. What transformations can be applied to logarithmic functions to shift their graphs?
3. How do you find the domain of a logarithmic function?
4. What are the characteristics of exponential and logarithmic graphs?
5. How do you determine the equation of a graph with an asymptote?

**Tip:** For identifying logarithmic functions, always look for key features like vertical asymptotes and slow growth rates after certain points on the x-axis.

Write an equation for the function graphed above.

Discover how to find the equation of a logarithmic function, y = ln(x + 1), with a vertical asymptote at x = -1. Learn the characteristics of logarithmic functions and how they relate to graphing. This problem is ideal for students in Grades 10-12.

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