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).