Let’s solve the questions step by step based on the given graph of $g(x)$.

(a) $g(-4)$, $g(-2)$, $g(0)$, $g(2)$, and $g(4)$:

1. $g(-4)$: From the graph, when $x = -4$, $g(-4) = 1$.
2. $g(-2)$: When $x = -2$, $g(-2) = -3$.
3. $g(0)$: When $x = 0$, $g(0) = 0$.
4. $g(2)$: When $x = 2$, $g(2) = 3$.
5. $g(4)$: When $x = 4$, $g(4) = -1$.

(b) Domain and Range of $g(x)$:

• Domain: The graph extends horizontally from $x = -4$ to $x = 4$, so $\text{Domain} = [-4, 4]$.
• Range: The vertical extent of the graph is from $y = -3$ to $y = 3$, so $\text{Range} = [-3, 3]$.

(c) Values of $x$ for which $g(x) = 3$:

From the graph, $g(x) = 3$ at $x = 2$ and $x = -3$.

(d) Values of $x$ for which $g(x) \leq 0$:

From the graph, $g(x) \leq 0$ for:

• $x \in [-3, 0]$ (from $x = -3$ to $x = 0$, including endpoints).

(e) Net change in $g(x)$ between $x = -1$ and $x = 2$:

• At $x = -1$, $g(-1) = -2$.
• At $x = 2$, $g(2) = 3$.
• Net change: $g(2) - g(-1) = 3 - (-2) = 5$.

Let me know if you would like a detailed explanation for any part or have further questions. Here are five follow-up questions you might find useful:

1. How can you verify the domain and range from the graph?
2. Why is the net change calculated as $g(2) - g(-1)$?
3. Can you determine if $g(x)$ is a one-to-one function?
4. How would you find where $g(x) > 0$ on this graph?
5. What would the slope of the tangent line represent for $g(x)$ at specific points?

Tip: Always observe whether a function is increasing or decreasing between points to better understand its behavior.