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.