https://file.aiquickdraw.com/mathbot/file/17266106818827n03px8x.jpg

To solve this problem, let's analyze the graph shown in the image to determine when the function is negative.

1. **Graph Analysis:**  
   The graph is a simple piecewise linear function. The function appears to cross the x-axis at two points:
   - One point seems to be at \( x = -6 \).
   - The other point seems to be at \( x = 2 \).

   The function dips below the x-axis (i.e., the function is negative) between these two points. This means that the function is negative for the interval:
   \[
   -6 < x < 2
   \]

2. **Answer Choices:**  
   The answer choices provided are:
   - \( x > 3 \)
   - \( x < 3 \)
   - \( -6 < x < 2 \)
   - \( x < -6 \) and \( x > 2 \)

   Based on the interval identified from the graph, the correct answer is:
   \[
   -6 < x < 2
   \]

   Therefore, the function is negative for the interval \( -6 < x < 2 \).

Would you like a more detailed explanation of this solution, or do you have any questions about the graph or the problem?

### Related Questions:
1. What does it mean for a function to be positive on a graph?
2. How can you find where a function is zero using its graph?
3. What are the steps to determine intervals of positivity and negativity for a given function?
4. How do piecewise functions affect the intervals of positivity and negativity?
5. How can the slope of a function affect its intervals of positivity and negativity?

**Tip:** When analyzing the graph of a function, focus on the x-axis intersections to identify intervals where the function changes its sign (positive or negative).

Learn how to analyze a graph to determine when a function is negative. This problem involves understanding intervals, inequalities, and interpreting the behavior of functions on a graph.

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