Let's analyze the graph provided and solve the equations and inequalities:

Part A: Find the solutions to the equation $f(x) = g(x)$.

We are looking for the points where the two functions intersect. Based on the graph:

• $f(x)$ is the blue line and $g(x)$ is the red line.
• The two lines intersect at points $(-3, 3)$ and $(3, 3)$.

Thus, the solutions to $f(x) = g(x)$ are: $x = -3, 3$

Part B: Find the solutions to the inequality $f(x) < g(x)$.

We are looking for where the blue line $f(x)$ is below the red line $g(x)$.

• From $x = -3$ to $x = 3$, $f(x)$ is below $g(x)$.

Thus, the solution in interval notation is: $(-3, 3)$

Part C: Find the solutions to the inequality $f(x) > g(x)$.

We are looking for where the blue line $f(x)$ is above the red line $g(x)$.

• For $x < -3$ and $x > 3$, $f(x)$ is above $g(x)$.

Thus, the solution in interval notation is: $(-\infty, -3) \cup (3, \infty)$

Final Answers:

• Part A: $x = -3, 3$
• Part B: $(-3, 3)$
• Part C: $(-\infty, -3) \cup (3, \infty)$

Let me know if you need further details or clarifications! Here are some related questions to think about:

1. What is the general approach to solving $f(x) = g(x)$ graphically?
2. How can you determine where one function is greater than another using a graph?
3. Can you explain how interval notation represents the solution set?
4. What happens if two functions don't intersect at any point?
5. How do vertical asymptotes affect the analysis of inequalities like $f(x) < g(x)$?

Tip: When solving inequalities graphically, always check where the curves cross and how they behave between the intersections.