https://file.aiquickdraw.com/mathbot/file/1726754686874x4xvddrq.jpg

The image shows a graph of a function \( y = g(x) \), along with a question related to the graph. Let's extract and interpret the graph and the first question.

### Understanding the Graph
- The graph shows a curve with several key features, including:
  - A smooth curve with both upward and downward sections.
  - Points where the function crosses the x-axis (roots).
  - Maximum and minimum points (peaks and troughs).
  - Vertical asymptote at \( x = 3 \) (the dashed red vertical line).

### Question A: "What is the domain of \( g(x) \)?"
The **domain** of a function refers to the set of all possible input values (x-values) for which the function is defined.

From the graph:
- The function is continuous and defined on all x-values except at \( x = 3 \), where there appears to be a vertical asymptote. This suggests that the function is undefined at this value.

Thus, the domain of \( g(x) \) is:
\[
\text{Domain of } g(x): (-\infty, 3) \cup (3, \infty)
\]
This means the function is defined for all real numbers except \( x = 3 \).

Would you like a detailed explanation of another part of the graph or another question from this quiz?

### Related Questions:
1. What are the x-intercepts of the graph (where \( g(x) = 0 \))?
2. What is the range of \( g(x) \)?
3. Identify the relative maximum and minimum points of \( g(x) \).
4. Describe the behavior of \( g(x) \) as \( x \to 3 \) from both sides.
5. What are the intervals where \( g(x) \) is increasing or decreasing?

### Tip:
When analyzing the domain of a function, always check for points of discontinuity such as vertical asymptotes, holes, or restrictions from square roots and logarithms.

Understand how to find the domain of the function g(x) from its graph, which includes a vertical asymptote at x = 3. This problem covers key concepts in function analysis, such as identifying points of discontinuity and vertical asymptotes. Suitable for students in Grades 9-12.

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