The problem asks to identify specific intervals and points where the values of $f(x)$ and $g(x)$ (shown in the graph) meet certain conditions, such as when one function is greater or less than the other.

The functions are as follows:

• $f(x)$: the solid line graph.
• $g(x)$: the dashed line graph.

Let’s break down the different conditions based on the graph:

1. Intervals where $g(x) < f(x)$:

   • This is asking where the dashed line graph $g(x)$ is below the solid line graph $f(x)$.
   • By inspecting the graph, $g(x)$ is below $f(x)$ in the interval: $(-\infty, -3) \cup (7, 25)$
   • These are the intervals where the dashed line lies below the solid line.

2. $g(x) = f(x)$ when $x = -6, 6$:

   • This asks to find the points where $g(x)$ equals $f(x)$, i.e., where the solid and dashed lines intersect.
   • Based on the graph, the functions intersect at $x = -6$ and $x = 6$.

3. $g(x) > f(x)$ on the interval $(-3, 7)$:

   • This asks where the dashed line $g(x)$ is above the solid line $f(x)$.
   • The graph shows that between $x = -3$ and $x = 7$, the dashed line is indeed above the solid line.

4. Intervals where $f(x) < 0$ on the interval $-7 \leq x \leq 10$:

   • This asks where the solid line $f(x)$ (solid graph) is below the x-axis (negative values).
   • Inspecting the graph, we see that $f(x)$ is negative for the interval: $(-5, 3.14)$
   • This means the solid line is below the x-axis between these values of $x$.

Let me know if you want further clarifications or details.

Here are 5 related questions you could explore:

1. What happens if we find intervals where both $f(x)$ and $g(x)$ are positive?
2. How would the intervals change if we were looking for $g(x) \leq f(x)$?
3. Can we generalize how to find intersections of two graphs in more complex functions?
4. What transformations would shift $g(x)$ above $f(x)$ in all intervals?
5. Can we determine the areas under $f(x)$ and $g(x)$ between given intervals?

Tip: Always sketch the graph yourself to visually check where one function is above or below the other to avoid mistakes in reading the graph.