Let's analyze the problem and graph in your image step by step:

The question asks you to:

1. Find the domain and range of g.
2. Use the formula to evaluate $g(-2)$ and $g(2)$.
3. Use the graph to evaluate $g(-2)$ and $g(2)$.
4. Find the domain of $g$ based on a given interval or notation choice.

From the graph provided:

• The domain of $g(x)$ refers to the set of all possible input values (x-values) where the graph is defined.

  • The graph seems to have endpoints at $x = -4$ and $x = 4$, meaning the domain is $[-4, 4]$.

• The range of $g(x)$ is the set of all possible output values (y-values) that the function can take.

  • By looking at the highest and lowest points of the graph, the range appears to be between $y = -2$ and $y = 3$, so the range is $[-2, 3]$.

For parts b and c:

• To evaluate $g(-2)$ and $g(2)$, simply locate these values on the graph.
  • At $x = -2$, the y-value on the graph is $1$, so $g(-2) = 1$.
  • At $x = 2$, the y-value is $-1$, so $g(2) = -1$.

Now for the multiple-choice part, select the domain based on the answer choices provided in the exercise (likely $[-4, 4]$).

Would you like to go over more details, or do you have any other questions about this?

Here are 5 follow-up questions for further exploration:

1. Can you describe the meaning of "range" in your own words?
2. What other methods can be used to find the range of a function?
3. What is the difference between discrete and continuous domains?
4. How does the shape of a graph influence its domain and range?
5. How would you determine $g(x)$ values if the graph were not provided?

Tip: Always check the endpoints on a graph carefully to define the domain and range correctly.