Let's go through the problems one by one based on the image provided.

(a) Finding the values of $h(x)$ for specific inputs:

From the graph, you can read the function values for the given $x$-values.

• $h(-2) = -1$
• $h(0) = -3$
• $h(2) = 2$
• $h(3) = 1$

(b) Domain and Range of $h$:

• Domain: The domain consists of all $x$-values for which the function is defined. From the graph, the function is defined from $x = -5$ to $x = 6$. So, the domain is: $[-5, 6]$

• Range: The range consists of all $y$-values that the function takes. From the graph, the minimum $y$-value is $-3$, and the maximum $y$-value is $4$. So, the range is: $[-3, 4]$

(c) Finding values of $x$ for which $h(x) = 2$:

From the graph, you can see that $h(x) = 2$ occurs at two points:

• $x = 2$
• $x = 4$

Thus, the values of $x$ are: $x = 2, 4$

(d) Finding values of $x$ for which $h(x) \leq 2$:

From the graph, $h(x) \leq 2$ occurs in the intervals:

• $x \in [-3, 2]$ and at $x = 4$

So, the correct answer is: $[-3, 2] \text{ and } 4$

(e) Finding the net change in $h$ between $x = -3$ and $x = 3$:

• $h(-3) = 0$
• $h(3) = 1$

The net change is: $h(3) - h(-3) = 1 - 0 = 1$

Do you have any questions about these answers or want more details on any step? Here are 5 related questions to expand on these topics:

1. How would you find the values of $x$ for which $h(x) = -1$?
2. Can you explain how to determine if a function is increasing or decreasing on a specific interval from a graph?
3. What would the graph look like if the range was extended to $[-5, 5]$?
4. How do you determine the derivative of a function given its graph?
5. Can you find the average rate of change of $h(x)$ between $x = -5$ and $x = 6$?

Tip: When analyzing a function's graph, always check where the function crosses key values like $y = 0$, since these intersections can provide critical points for solving equations.