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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).

The entire graph of the function h is shown in the figure below. Write the domain and range of h using interval notation.

Learn how to determine the domain and range of a function represented by a parabola. This problem focuses on graph analysis and understanding interval notation, suitable for students in Grades 9-10.

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