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We are given that the function \( h(x) \) is graphed, and the point \( (3, -2) \) is on the graph of \( y = h(x) \). Now, we need to find which of the points is on the graph of \( y = 2h(x) - 1 \).

### Step-by-step process:

1. **Original function information**: We know that \( h(3) = -2 \) because the point \( (3, -2) \) is on the graph of \( y = h(x) \).
   
2. **Transformation of the function**: The new function is \( y = 2h(x) - 1 \). To find the corresponding point for \( x = 3 \) in the new function:
   - Start with \( h(3) = -2 \).
   - Substitute \( h(3) \) into the new function:
     \[
     y = 2h(3) - 1 = 2(-2) - 1 = -4 - 1 = -5.
     \]
   - Thus, the point \( (3, -5) \) is on the graph of the transformed function \( y = 2h(x) - 1 \).

### Conclusion:
The correct point that lies on the graph of \( y = 2h(x) - 1 \) is \( (3, -5) \), which corresponds to option **B**.

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Would you like further details on any part of the solution?

Here are 5 related questions to deepen your understanding:
1. How does multiplying a function by a constant affect its graph?
2. What happens when you subtract a constant from a function?
3. How can transformations of functions be identified based on the equation?
4. How would the graph of \( y = -2h(x) + 3 \) be transformed compared to \( y = h(x) \)?
5. What is the general form of function transformations, and how can you apply them?

**Tip:** Always carefully apply transformations step by step to ensure you're correctly interpreting how each change affects the graph!

In the xy-plane, the function h is graphed on the interval 0 ≤ x ≤ 10. The point (3, -2) is on the graph of y = h(x). Which of the following points is on the graph of y = 2h(x) - 1?

Learn how to determine a point on the graph of the transformed function y = 2h(x) - 1 given a point on y = h(x). This algebraic problem covers key concepts related to function transformations. Suitable for students in Grades 9-11.

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