The image shows a math question asking to graph the function $f(x) = \log_3(x - 2)$ using the graph of $f(x) = \log_3(x)$.

To help with this:

1. Original Function: The function $f(x) = \log_3(x)$ is the base logarithmic function with base 3. Its graph has the following characteristics:

   • Domain: $x > 0$
   • Vertical asymptote: $x = 0$
   • The graph passes through $(1, 0)$, since $\log_3(1) = 0$.

2. Transformation: The new function $f(x) = \log_3(x - 2)$ represents a horizontal shift of the graph $\log_3(x)$ to the right by 2 units.

   • Domain: $x > 2$ (since the argument of the logarithm, $x - 2$, must be positive)
   • Vertical asymptote: The asymptote moves from $x = 0$ to $x = 2$.

So, to graph $f(x) = \log_3(x - 2)$:

• Take the graph of $\log_3(x)$ and shift every point 2 units to the right.
• The new graph will have a vertical asymptote at $x = 2$, and it will still pass through points like $(3, 0)$, since $\log_3(3 - 2) = 0$.

Would you like to know more details or ask further questions? Here are some related questions:

1. How do horizontal shifts affect the domain of a function?
2. What is the general formula for a horizontal shift in logarithmic functions?
3. How does a vertical shift change the graph of a logarithmic function?
4. What other types of transformations can be applied to logarithmic functions?
5. How can we find the x-intercept of the transformed function?

Tip: When graphing logarithmic functions, always check for vertical asymptotes and intercepts, as they give valuable information about the function's behavior.