The graph provided represents a function $h(x)$, and we are tasked with finding the domain and range of this function. Let's analyze the graph:

1. Domain (x-values):

• The domain represents all possible $x$-values for which the function is defined.
• From the graph, we can observe that the function starts at around $x = -6$ and continues up to approximately $x = 2$. Therefore, the domain of the function $h(x)$ can be written as: $\text{Domain of } h: \ [-6, 2]$

2. Range (y-values):

• The range represents all possible $y$-values that the function attains.
• The graph shows that the lowest point on the graph occurs at around $y = -4$, and the highest point is approximately $y = 5$.
• Therefore, the range of the function $h(x)$ can be written as: $\text{Range of } h: \ [-4, 5]$

Thus, the domain and range of the function $h(x)$ are:

• Domain: $[-6, 2]$
• Range: $[-4, 5]$

Would you like more details or have any questions? Here are some related questions you could explore:

1. What would the domain and range look like for different types of functions, such as quadratic or exponential?
2. How can you determine the domain and range of a function algebraically without a graph?
3. What happens to the domain and range if the function is transformed (e.g., translated, reflected)?
4. How can you express domain and range for piecewise functions?
5. What are the key differences between the domain and range of continuous vs. discrete functions?

Tip: When analyzing the domain of a function, always check for undefined points (e.g., where the denominator could be zero or square roots of negative numbers).