https://file.aiquickdraw.com/mathbot/file/1730206027545hu6mblnw.jpg

To solve this question, let's analyze the given information.

The problem states:
- **Equation**: \( y = \left( \frac{1}{2} \right)^x \)
- **Graph**: The question asks if the given graph represents the equation \( y = \left( \frac{1}{2} \right)^x \).

### Step-by-Step Analysis:
1. **Function Type**:
   - The equation \( y = \left( \frac{1}{2} \right)^x \) represents an **exponential decay function** because the base \( \frac{1}{2} \) is between 0 and 1.
   - This type of function generally decreases as \( x \) increases.

2. **Expected Graph Shape**:
   - For \( y = \left( \frac{1}{2} \right)^x \):
     - As \( x \to +\infty \), \( y \to 0 \) (the graph approaches the x-axis from above).
     - As \( x \to -\infty \), \( y \to +\infty \) (the graph rises sharply for negative \( x \) values).

3. **Graph Observation**:
   - The graph shown in the image appears to be increasing as \( x \) increases, which is characteristic of an **exponential growth** function, not exponential decay.
   - This suggests the graph might represent a function like \( y = 2^x \), where the base is greater than 1, rather than \( y = \left( \frac{1}{2} \right)^x \).

### Conclusion:
The statement in the question is **false**. The graph does **not** represent the function \( y = \left( \frac{1}{2} \right)^x \).

Would you like more details or have any further questions?

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Here are 5 related questions:
1. What are the characteristics of exponential growth and decay functions?
2. How does the base of an exponential function affect its graph?
3. What are some real-world examples of exponential decay?
4. How can we determine the y-intercept of an exponential function?
5. How do transformations affect the graph of an exponential function?

**Tip**: For exponential functions, if the base is between 0 and 1, the function represents decay; if the base is greater than 1, it represents growth.

اختر (صواب) أو (خطأ) للعبارة الآتية: التمثيل البياني للدالة y = (1/2)^x هو (صواب أم خطأ؟)

Analyze whether the given graph represents the exponential decay function y = (1/2)^x. Understand the characteristics of exponential decay and distinguish it from exponential growth. Suitable for students in Grades 9-11.

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