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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.

Use the graph of f(x) = log_3(x) to graph the function f(x) = log_3(x - 2).

Learn how to graph the logarithmic function f(x) = log_3(x - 2) by using the graph of f(x) = log_3(x) and applying a horizontal shift of 2 units to the right. This tutorial is perfect for students in Grades 9-12 studying transformations of logarithmic functions.

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