Here is the graph of the function $y = \ln(x - 1) + 4$, showing the vertical asymptote at $x = 1$, the point $(2, 4)$, and the general shape of the curve.

Would you like any further clarification on this graph, or do you have other questions?

Related Questions:

1. How does the transformation of the logarithmic function affect its graph?
2. What happens to the graph of $y = \ln(x - a) + b$ when we change $a$ or $b$?
3. How can you solve for $x$ when $y = \ln(x - 1) + 4$?
4. What is the relationship between exponential and logarithmic functions?
5. Can you explain the concept of a vertical asymptote in logarithmic graphs?

Tip:

When graphing logarithmic functions, remember that shifts and translations do not affect the domain restrictions. Always check for the values that make the argument of the logarithm positive!