To graph the function \( y = -h(x + 2) \), follow these steps:

1. **Understand the transformation**:  
   The function \( y = -h(x + 2) \) represents a transformation of the basic function \( y = h(x) \).

   - \( x + 2 \) shifts the graph of \( y = h(x) \) horizontally to the left by 2 units.
   - The negative sign in front of \( h(x + 2) \) reflects the graph across the x-axis.

2. **Start with the base graph**:  
   Begin by sketching the graph of the base function \( y = h(x) \). Since \( h(x) \) is not specified, we'll consider it as a generic function.

3. **Apply the transformations**:
   - **Horizontal Shift**: Shift the graph of \( y = h(x) \) left by 2 units. This means each point \((x, y)\) on the graph of \( y = h(x) \) moves to \((x - 2, y)\).
   - **Reflection**: Reflect the graph obtained in the previous step across the x-axis. This means if a point \((x, y)\) was on the graph before reflection, it now moves to \((x, -y)\).

4. **Sketch the final graph**:  
   Combine the transformations to produce the graph of \( y = -h(x + 2) \).

### Example:
If \( y = h(x) \) was \( y = x^2 \) (a simple parabola):

- The graph of \( y = h(x) = x^2 \) is a parabola opening upwards with its vertex at the origin (0,0).
- Applying \( x + 2 \) shifts it left to center the vertex at (-2, 0).
- Reflecting it across the x-axis inverts it, turning it into a downward-opening parabola centered at (-2, 0).

Would you like more details on a specific type of function for \( h(x) \) or have any questions?

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Here are some follow-up questions:

1. What specific function would you like to use for \( h(x) \)?
2. How does the horizontal shift of a function affect its graph?
3. Can you explain the effect of a vertical reflection on a function’s graph?
4. How would the graph change if the function were \( y = -h(x - 2) \)?
5. What if we had \( y = h(-x + 2) \) instead?
6. How do horizontal and vertical transformations differ in their impact on the graph?
7. What does the graph look like if \( h(x) \) is a linear function?
8. What would the graph look like if \( h(x) \) is a trigonometric function like sine or cosine?

**Tip**: Always consider the order of transformations when graphing complex functions, as it can significantly affect the final result.

Learn how to graph the function y = -h(x + 2) with detailed step-by-step instructions. Understand horizontal shifts and reflections in function graphs. Suitable for high school students studying graph transformations.

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