To solve the problem, we need to determine over which intervals the function is positive (above the x-axis) and negative (below the x-axis) based on the graph.

Analysis of the Graph:

1. The graph crosses the x-axis at two points:

   • At $x = -2$
   • At $x = 4$

2. Positive intervals (when the function is above the x-axis):

   • The function is above the x-axis between $x = -2$ and $x = 4$.
   • Therefore, the positive interval is $(-2, 4)$.

3. Negative intervals (when the function is below the x-axis):

   • The function is below the x-axis for $x < -2$ and for $x > 4$.
   • Thus, the negative intervals are $(-\infty, -2) \cup (4, \infty)$.

Final Answer:

• The function is positive in the interval $(-2, 4)$.
• The function is negative in the intervals $(-\infty, -2)$ and $(4, \infty)$.

Would you like further details on how to analyze graphs like this?

Here are some related questions to explore:

1. How do we determine if a function is increasing or decreasing from a graph?
2. How do the x-intercepts of a graph relate to the intervals of positivity and negativity?
3. What is the significance of the slope of the line in this graph?
4. How do we find the vertex or turning point of a linear graph?
5. What is the general form of a piecewise function that would represent this graph?

Tip: Always look at the x-axis intersections to determine where the function changes from positive to negative or vice versa.