The graph you provided is a parabola that opens downward. To determine the domain and range of the function $h$, we can analyze the graph as follows:

1. Domain:

The domain represents all possible input values (x-values) for the function.

• From the graph, it appears that the parabola extends horizontally from $x = -3$ to $x = 3$.
• Therefore, the domain of the function is: $\boxed{[-3, 3]}$

2. Range:

The range represents all possible output values (y-values) for the function.

• The highest point (the vertex) of the parabola is at $y = 1$, and the lowest point (the endpoints) is at $y = -4$.
• Therefore, the range of the function is: $\boxed{[-4, 1]}$

Would you like further details or have any questions?

Here are some related questions you might want to explore:

1. How can we find the vertex of a parabola algebraically?
2. What is the general form of a quadratic function?
3. How do we determine whether a parabola opens upwards or downwards?
4. Can the range of a quadratic function ever be unbounded?
5. How would the domain and range change if the parabola were shifted?

Tip: The vertex form of a parabola, $y = a(x - h)^2 + k$, provides valuable information about the parabola's vertex and its orientation (upward or downward).