Let's analyze the graph and solve the questions one by one:

1. The function $g(x)$ is shown on the graph.

   a) Find $g(2)$:

   • Looking at $x = 2$ on the graph, the value of $g(2)$ is approximately 6.

   b) Find $g(-3)$:

   • At $x = -3$, the value of $g(-3)$ is 0 (as the point crosses the x-axis at this point).

   c) Find the value of $g(2) + g(1)$:

   • We already found that $g(2) = 6$.
   • For $g(1)$, looking at $x = 1$ on the graph, the value is 7.
   • So, $g(2) + g(1) = 6 + 7 = 13$.

   d) Find the value(s) of $x$ when $g(x) = 0$:

   • $g(x) = 0$ where the graph crosses the x-axis.
   • This happens at $x = -3$ and $x = 4$.
   • So, $x = -3$ and $x = 4$.

   e) Find the value(s) of $x$ when $g(x) = -2$:

   • Look for where the graph hits $g(x) = -2$ on the y-axis.
   • This happens at $x = -5$ and $x = -1$.
   • So, $x = -5$ and $x = -1$.

   f) State the domain of the function:

   • The domain is the set of all possible $x$-values.
   • Based on the graph, the function is defined for $x$ values between $-5$ and $5$.
   • So, the domain is $[-5, 5]$.

   g) State the range of the function:

   • The range is the set of all possible $y$-values.
   • From the graph, the function takes values between $-4$ and $7$.
   • So, the range is $[-4, 7]$.

Would you like further details on any part of this? Here are some related questions for deeper understanding:

1. How can you determine the domain and range of a function from a graph?
2. What are the important features of a graph (e.g., intercepts, increasing/decreasing intervals)?
3. How would you express a function that passes through certain points as an equation?
4. What happens if the graph is shifted up or down? How does that affect the range?
5. Can you find the inverse of this function based on its graph?

Tip: Always check the x-intercepts and y-intercepts of a graph to easily identify when the function equals 0 and the domain/range limits.