The given graph shows a transformation of a basic function, and we are tasked with finding the equation.

Observing the graph:

1. The blue curve appears to represent the graph of a logarithmic function, which usually takes the form: $y = \log_b(x - h) + k$ where:
   • $b$ is the base of the logarithm.
   • $h$ is the horizontal shift.
   • $k$ is the vertical shift.

Analyzing the graph:

• The curve approaches the vertical line $x = 5$, which suggests a horizontal shift of 5 units to the right. This gives the factor $(x - 5)$.
• The graph appears to reflect across the x-axis, which would indicate a negative sign.
• The vertical shift appears to be 0, meaning there's no upward or downward translation.

Conclusion:

The equation of the graph is likely of the form: $y = -\log(x - 5)$

Let me know if you need more detailed reasoning or clarifications!

Here are 5 related questions to consider:

1. How would the equation change if there were a vertical shift in the graph?
2. What happens to the graph if the base of the logarithm changes (e.g., $\log_2$ instead of $\log$)?
3. How would the graph transform if we change the sign of the coefficient of $x$?
4. What are the general transformations that can be applied to any logarithmic function?
5. How can you verify if the transformation involves a reflection over the x-axis or y-axis?

Tip: When determining the equation from a transformed graph, always look for horizontal and vertical shifts first, followed by any reflections or stretches.