Let's go through each part of the problem using the graphs provided:

1. Identifying the functions:
   • The blue line represents $y = f(x)$.
   • The red line represents $y = g(x)$.

Solutions

(a) Solve $g(x) = 0$:

• To find where $g(x) = 0$, we look for points on the red line where it crosses the x-axis.
• From the graph, $g(x) = 0$ when $x = 0$.

Answer: $x = 0$.

(b) Solve $g(x) \geq 0$:

• For $g(x) \geq 0$, we are looking for intervals where the red line is above or on the x-axis.
• From the graph, $g(x)$ is non-negative for $x$ in the interval $[0, 8]$.

Answer: $[0, 8]$.

(c) Solve $f(x) < 0$:

• To determine where $f(x) < 0$, we look for portions of the blue line below the x-axis.
• From the graph, $f(x)$ is less than zero for $x$ in the interval $(-8, -4)$.

Answer: $(-8, -4)$.

Would you like a more detailed explanation of any part?

Here are some related questions that may interest you:

1. How would the solutions change if we needed $g(x) > 0$ instead of $g(x) \geq 0$?
2. Can you find intervals where both $f(x)$ and $g(x)$ are positive?
3. What are the intervals where $f(x)$ and $g(x)$ intersect?
4. How would you describe the symmetry (if any) in $f(x)$ and $g(x)$?
5. Could you find the slopes of $f(x)$ and $g(x)$ at certain intervals?

Tip: When solving inequalities graphically, remember to focus on where the function is positioned relative to the x-axis and its respective range.